Title: Chapter 7
Course: quiz duplicate error

Q: Find the geometric mean between each pair of numbers.
28 and 7
- [Image] (Find the product of the given numbers. Find the square root of the product.)
- 196 (Find the product of the given numbers. Find the square root of the product.)
- [Image] (Find the product of the given numbers. Find the square root of the product.)
- 17.5 (Find the product of the given numbers. Find the square root of the product.)
A: [Image]

Q: Find x.
[Image]
- 22 (The sum of the squares of the two sides is equal to the square of the hypotenuse.)
- [Image] (The sum of the squares of the two sides is equal to the square of the hypotenuse.)
- 1144 (The sum of the squares of the two sides is equal to the square of the hypotenuse.)
- [Image] (The sum of the squares of the two sides is equal to the square of the hypotenuse.)
A: [Image]

Q: Find the geometric mean between each pair of numbers.
[Image] and [Image]
- 22.5 (Find the product of the given numbers. Find the square root of the product.)
- [Image] (Find the product of the given numbers. Find the square root of the product.)
- 464 (Find the product of the given numbers. Find the square root of the product.)
- [Image] (Find the product of the given numbers. Find the square root of the product.)
A: [Image]

Q: Determine whether [Image] is a right triangle for the given vertices. Explain.

Q(18, 13), R(17, –3), S(–18, 12)
- no; QR = [Image], QS = [Image], RS = [Image]; QR^2 + QS^2 ¹ RS^2 (Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter sides is equal to the square of the third side, the triangle is a right triangle.)
- yes; QR = [Image], QS = [Image], RS = [Image]; RS^2 + QS^2 = RQ^2 (Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter sides is equal to the square of the third side, the triangle is a right triangle.)
- yes; QR = [Image], QS = [Image], RS = [Image]; QR^2 + QS^2 ¹ RS^2 (Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter sides is equal to the square of the third side, the triangle is a right triangle.)
- no; QR = [Image], QS = [Image], RS = [Image]; RS^2 + QS^2 = RQ^2 (Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter sides is equal to the square of the third side, the triangle is a right triangle.)
A: no; QR = [Image], QS = [Image], RS = [Image]; QR^2 + QS^2 ¹ RS^2

Q: Find x, y, and z.
[Image]
- x » 13.7, y » 31.5, z » 37.5 (The altitude is the geometric mean between the measures of the two segments of the hypotenuse.)
- x » 37.5, y » 13.7, z » 31.5 (The altitude is the geometric mean between the measures of the two segments of the hypotenuse.)
- x » 31.5, y » 37.5, z » 13.7 (The altitude is the geometric mean between the measures of the two segments of the hypotenuse.)
- x » 13.7, y » 31.5, z » 37.5 (The altitude is the geometric mean between the measures of the two segments of the hypotenuse.)
A: x » 13.7, y » 31.5, z » 37.5

Q: Determine whether [Image] is a right triangle for the given vertices. Explain.

Q(–6, –2), R(2, –5), S(–3, 6)
- no; QR = [Image], QS = [Image], RS = [Image]; QR^2 + QS^2 ¹ RS^2 (Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter sides is equal to the square of the third side, the triangle is a right triangle.)
- yes; QR = [Image], QS = [Image], RS = [Image]; QR^2 + QS^2 = RS^2 (Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter sides is equal to the square of the third side, the triangle is a right triangle.)
- yes; QR = [Image], QS = [Image], RS = [Image]; RS^2 + QS^2 = RQ^2 (Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter sides is equal to the square of the third side, the triangle is a right triangle.)
- no; QR = [Image], QS = [Image], RS = [Image]; RS^2 + QS^2 ¹ RQ^2 (Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter sides is equal to the square of the third side, the triangle is a right triangle.)
A: yes; QR = [Image], QS = [Image], RS = [Image]; QR^2 + QS^2 = RS^2

Q: Find x.
[Image]
- 6 (Divide the large triangle into two right triangles. Which side is the hypotenuse? Which sides are the legs? Substitute the values into the Pythagorean Theorem to solve for the missing variable.)
- 16 (Divide the large triangle into two right triangles. Which side is the hypotenuse? Which sides are the legs? Substitute the values into the Pythagorean Theorem to solve for the missing variable.)
- [Image] (Divide the large triangle into two right triangles. Which side is the hypotenuse? Which sides are the legs? Substitute the values into the Pythagorean Theorem to solve for the missing variable.)
- [Image] (Divide the large triangle into two right triangles. Which side is the hypotenuse? Which sides are the legs? Substitute the values into the Pythagorean Theorem to solve for the missing variable.)
A: [Image]

Q: Find the measure of the altitude.
[Image]
- [Image] (The altitude is the geometric mean between the measures of the two segments of the hypotenuse.)
- 11.5 (The altitude is the geometric mean between the measures of the two segments of the hypotenuse.)
- [Image] (The altitude is the geometric mean between the measures of the two segments of the hypotenuse.)
- 120 (The altitude is the geometric mean between the measures of the two segments of the hypotenuse.)
A: [Image]

Q: A 60-yard long drawbridge has one end at ground level. The other end is initially at an incline of 5°.

During one stage of the drawbridge’s motion, the raised end is 11 yards above the ground. What is the incline of the drawbridge to the nearest hundredth?
- 10.39° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 10.56° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 21.56° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 79.44° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 10.56°

Q: A space shuttle is one kilometer above sea level when it begins to climb at a constant angle of 3° for the next 80 ground kilometers. About how far above sea level is the space shuttle after its climb?
- 4.2 kilometers (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 5.2 kilometers (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 79.9 kilometers (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 80.9 kilometers (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 5.2 kilometers

Q: A dog chasing some birds in the woods got away from its owner. If the owner is 30 feet lower than the dog and the angle of elevation from the owner to the dog is 10°, find the distance from the owner to the dog.
- 19.47 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 30.46 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 170.14 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 172.76 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 172.76 ft

Q: A 60-yard long drawbridge has one end at ground level. The other end is initially at an incline of 5°.

During one stage of the drawbridge’s motion, the raised end is 15 yards above the ground. What is the incline of the drawbridge to the nearest hundredth?
- 0.004° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 14.04° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 14.48° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 75.52° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 14.48°

Q: Find the measure of each angle to the nearest tenth of a degree.
[Image]
- 30.9 (In trigonometry, you can find the measure of an angle by using the inverse of sine, cosine, or tangent.)
- 59.1 (In trigonometry, you can find the measure of an angle by using the inverse of sine, cosine, or tangent.)
- 0.5135 (In trigonometry, you can find the measure of an angle by using the inverse of sine, cosine, or tangent.)
- 27.2 (In trigonometry, you can find the measure of an angle by using the inverse of sine, cosine, or tangent.)
A: 59.1

Q: Lynn is standing at horizontal ground level with the base of the Sears Tower in Chicago. The angle formed by the ground and the line segment from her position to the top of the building is 15.7°. The height of the Sears Tower is 1450 feet. Find her distance from the Sears Tower to the nearest foot.
- 408 feet (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 7 feet (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 5159 feet (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 5358 feet (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 5159 feet

Q: Find x and y.
[Image]
- [Image] (The length of the hypotenuse is equal to the length of a leg times [Image]. The diagonal of a square bisects the angle.)
- [Image] (The length of the hypotenuse is equal to the length of a leg times [Image]. The diagonal of a square bisects the angle.)
- [Image] (The length of the hypotenuse is equal to the length of a leg times [Image]. The diagonal of a square bisects the angle.)
- [Image] (The length of the hypotenuse is equal to the length of a leg times [Image]. The diagonal of a square bisects the angle.)
A: [Image]

Q: A 60-yard long drawbridge has one end at ground level. The other end is initially at an incline of 5°.

During one stage of the drawbridge’s motion, the raised end is 12 yards above the ground. What is the incline of the drawbridge to the nearest hundredth?
- 11.31° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 11.54° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 78.46° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 78.69° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 11.54°

Q: A landscaper is making a retaining wall to shore up the side of a hill. To ensure against collapse, the wall should make an angle 75° or less with the ground.

If the wall is 15 feet, what is the height of the hill?
- 55.98 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 15.53 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 14.49 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 3.88 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 14.49 ft

Q: Determine whether the set of numbers can be the measures of the sides of a right triangle. Then state whether they form a Pythagorean Triple.
[Image], [Image], [Image]
- no, yes (Substitute the values into the Pythagorean Theorem to determine if the sides form a right triangle. The largest value is c. If the numbers are whole numbers, then the numbers form a Pythagorean Triple.)
- yes, yes (Substitute the values into the Pythagorean Theorem to determine if the sides form a right triangle. The largest value is c. If the numbers are whole numbers, then the numbers form a Pythagorean Triple.)
- yes, no (Substitute the values into the Pythagorean Theorem to determine if the sides form a right triangle. The largest value is c. If the numbers are whole numbers, then the numbers form a Pythagorean Triple.)
- no, no (Substitute the values into the Pythagorean Theorem to determine if the sides form a right triangle. The largest value is c. If the numbers are whole numbers, then the numbers form a Pythagorean Triple.)
A: yes, no

Q: Use the figure to find the trigonometric ratio below. Express the answer as a decimal rounded to the nearest ten-thousandth.

[Image]
AC = [Image], CB = [Image], AD = 11, CD = 2, DB = 1

cos B
- 2.2361 (Determine the ratio associated with the given trigonometric term. Divide the numerator by the denominator.)
- 0.9839 (Determine the ratio associated with the given trigonometric term. Divide the numerator by the denominator.)
- 0.4472 (Determine the ratio associated with the given trigonometric term. Divide the numerator by the denominator.)
- 0.8944 (Determine the ratio associated with the given trigonometric term. Divide the numerator by the denominator.)
A: 0.4472

Q: A hiker stops to rest and sees a deer in the distance. If the hiker is 48 yards lower than the deer and the angle of elevation from the hiker to the deer is 15°, find the distance from the hiker to the deer.
- 18.21 yd (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 49.69 yd (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 179.14 yd (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 185.46 yd (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 185.46 yd

Q: While paddling a canoe up the river, Jan saw some beautiful flowers along the river bank. The canoe is 35 yards lower than the flowers. The distance from the canoe to the flowers is 225 yards. What is the angle of elevation?
- 8.8° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 8.9° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 81.1° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 81.2° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 8.9°

Q: A 60-yard long drawbridge has one end at ground level. The other end is initially at an incline of 5°.

How far off the ground is the raised end of the drawbridge in its initial setting?
- 5.23 yd (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 59.77 yd (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 685.80 yd (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 688.42 yd (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 5.23 yd

Q: A landscaper is making a retaining wall to shore up the side of a hill. To ensure against collapse, the wall should make an angle 75° or less with the ground.

How far from the base of the hill is the base of a 25-foot slanted wall?
- 6.5 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 24.1 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 93.3 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 96.6 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 6.5 ft

Q: A 60-yard long drawbridge has one end at ground level. The other end is initially at an incline of 5°.

During one stage of the drawbridge’s motion, the raised end is 18 yards above the ground. What is the incline of the drawbridge to the nearest hundredth?
- 0.005° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 16.70° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 17.46° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 72.54° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 17.46°

Q: Two horses are observed by a hang glider 80 meters above a meadow. The angles of depression are 10.4° and 8°. How far apart are the horses?
- 133.3 m (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 435.9 m (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 569.2 m (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 1005.1 m (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 133.3 m

Q: A bird watcher spied a woodpecker. The bird watcher is 40 yards lower than the woodpecker. The distance from the bird watcher to the woodpecker is 175 yards. What is the angle of elevation?
- 12.9° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 13.2° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 76.8° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 77.1° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 13.2°

Q: A hot air balloon is one mile above sea level when it begins to climb at a constant angle of 4° for the next 50 ground miles. About how far above sea level is the hot air balloon after its climb?
- 2.5 miles (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 3.5 miles (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 4.5 miles (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 716.03 miles (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 4.5 miles

Q: Two cabins are observed by a ranger in a 60 feet tower above a park. The angles of depression are 11.6° and 9.4°. How far apart are the cabins?
- 70.1 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 292.3 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 362.4 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 654.7 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 70.1 ft

Q: Pat was flying a kite when the string broke and the kite fell to the ground. Pat is 36 yards lower than the kite. The distance from Pat to the kite is 200 yards. What is the angle of elevation?
- 10.2° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 10.4° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 79.6° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 79.8° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 10.4°

Q: Dante is standing at horizontal ground level with the base of the Empire State Building in New York City. The angle formed by the ground and the line segment from his position to the top of the building is 48.4°. The height of the Empire State Building is 1472 feet. Find his distance from the Empire State Building to the nearest foot.
- 1307 (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 7.65 (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 2217 (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 1968 (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 1307

Q: Determine whether the set of numbers can be the measures of the sides of a right triangle. Then state whether they form a Pythagorean Triple.
10, 24, 26
- no, no (Substitute the values into the Pythagorean Theorem to determine if the sides form a right triangle. The largest value is c. If the numbers are whole numbers, then the numbers form a Pythagorean Triple.)
- no, yes (Substitute the values into the Pythagorean Theorem to determine if the sides form a right triangle. The largest value is c. If the numbers are whole numbers, then the numbers form a Pythagorean Triple.)
- yes, yes (Substitute the values into the Pythagorean Theorem to determine if the sides form a right triangle. The largest value is c. If the numbers are whole numbers, then the numbers form a Pythagorean Triple.)
- yes, no (Substitute the values into the Pythagorean Theorem to determine if the sides form a right triangle. The largest value is c. If the numbers are whole numbers, then the numbers form a Pythagorean Triple.)
A: yes, yes

Q: The length of a diagonal of a square is [Image] millimeters. Find the perimeter of the square.
- 576 millimeters (To find the leg of a 45-45-90 triangle when the hypotenuse is given, divide the hypotenuse by [Image]. To find the perimeter of the square, find the sum of all the sides.)
- [Image] millimeters (To find the leg of a 45-45-90 triangle when the hypotenuse is given, divide the hypotenuse by [Image]. To find the perimeter of the square, find the sum of all the sides.)
- 96 millimeters (To find the leg of a 45-45-90 triangle when the hypotenuse is given, divide the hypotenuse by [Image]. To find the perimeter of the square, find the sum of all the sides.)
- 1152 millimeters (To find the leg of a 45-45-90 triangle when the hypotenuse is given, divide the hypotenuse by [Image]. To find the perimeter of the square, find the sum of all the sides.)
A: 96 millimeters

Q: A landscaper is making a retaining wall to shore up the side of a hill. To ensure against collapse, the wall should make an angle 75° or less with the ground.

How far from the base of the hill is the base of a 15-foot slanted wall?
- 3.88 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 14.49 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 55.98 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 57.96 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 3.88 ft

Q: A traffic helicopter pilot 60 meters above the road spotted two antique cars. The angles of depression are 10.2° and 8.7°. How far apart are the cars?
- 58.6 m (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 392.1 m (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 333.5 m (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 725.6 m (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 58.6 m

Q: A rocket ship is two miles above sea level when it begins to climb at a constant angle of 3.5° for the next 40 ground miles. About how far above sea level is the rocket ship after its climb?
- 2.4 miles (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 4.4 miles (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 653.9 miles (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 655.9 miles (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 4.4 miles

Q: Find x and y.
[Image]
- [Image] (The shorter leg is half the length of the hypotenuse. The longer leg is [Image] times the length of the shorter leg.)
- [Image] (The shorter leg is half the length of the hypotenuse. The longer leg is [Image] times the length of the shorter leg.)
- [Image] (The shorter leg is half the length of the hypotenuse. The longer leg is [Image] times the length of the shorter leg.)
- [Image] (The shorter leg is half the length of the hypotenuse. The longer leg is [Image] times the length of the shorter leg.)
A: [Image]

Q: Dolores is standing on a horizontal ground level with the base of the Statue of Liberty in New York City. The angle formed by the ground and the line segment from her position to the top of the statue is 26.3°. The height of the Statue of Liberty is approximately 93 m. Find her distance from the Statue of Liberty to the nearest meter.
- 188 meters (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 0.005 meter (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 104 meters (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 210 meters (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 188 meters

Q: A landscaper is making a retaining wall to shore up the side of a hill. To ensure against collapse, the wall should make an angle 75° or less with the ground.

If the wall is 25 feet, what is the height of the hill?
- 6.5 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 24.1 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 25.9 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 93.3 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 24.1 ft

Q: Find x and y.
[Image]
- [Image] (The shorter leg is half the length of the hypotenuse. The longer leg [Image] times the length of the shorter leg.)
- [Image] (The shorter leg is half the length of the hypotenuse. The longer leg [Image] times the length of the shorter leg.)
- [Image] (The shorter leg is half the length of the hypotenuse. The longer leg [Image] times the length of the shorter leg.)
- [Image] (The shorter leg is half the length of the hypotenuse. The longer leg [Image] times the length of the shorter leg.)
A: [Image]

Q: Trevor, Robert, and Maurice made some paper airplanes and want to see how far they will fly. The distance from Trevor to Robert is 13.5 feet. The distance from Robert to Maurice is 14.2 feet. The distance from Maurice to Trevor is 6.6 feet. Find the measures of the three angles in the triangle.
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
A: [Image], [Image], [Image]

Q: Members of the soccer team are trying to map out some new plays before their next game. The goal is 24 feet wide.

Nina put a player 25 feet from one goal post and 35 feet from the other post. What is the player’s angle to make a shot on goal?
- 43.3 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 45.6 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 91.1 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 1274 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
A: 43.3

Q: Zack, Rachel, and Maddie are unraveling a huge ball of yarn to see how long it is. As they move away from each other, they form a triangle. The distance from Zack to Rachel is 3 meters. The distance from Rachel to Maddie is 2.5 meters. The distance from Maddie to Zack is 4 meters. Find the measures of the three angles in the triangle.
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
A: [Image], [Image], [Image]

Q: Tomas, Ling, and Daniel are experimenting with a giant rubber band. They each hold the rubber band to create a triangle. The distance from Tomas to Ling is 24 inches. The distance from Ling to Daniel is 36 inches. The distance from Daniel to Tomas is 20 inches. Find the measures of the three angles in the triangle.
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
A: [Image], [Image], [Image]

Q: Two observation stations that are 28 miles apart located a hot air balloon at the same time. The first station indicated that the position of the balloon made an angle of 52° with the line between the stations. The second station indicated that it made an angle of 54° with the same line. How far is the second station from the hot air balloon?
- 23 mi (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
- 23.6 mi (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
- 28 mi (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
- 74 mi (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
A: 23 mi

Q: A tubing run is 150 yards long with a vertical drop of 21.6 yards. Find the angle of depression of the run.
- 8.2° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 8.3° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 81.7° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 81.8° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 8.3°

Q: Tiffany, Lori, and Mika are practicing for an egg-toss contest. The distance from Tiffany to Lori is 17 inches. The distance from Lori to Mika is 32 inches. The distance from Mika to Tiffany is 28 inches. Find the measures of the three angles in the triangle.
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
A: [Image], [Image], [Image]

Q: A playground is situated on a triangular plot of land. Two sides of the plot are 175 feet long and they meet at an angle of 70°. For safety reasons, a fence is to be placed along the perimeter of the property. How much fencing material is needed?
- 110 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing side. Find the perimeter.)
- 200.8 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing side. Find the perimeter.)
- 375.8 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing side. Find the perimeter.)
- 550.8 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing side. Find the perimeter.)
A: 550.8 ft

Q: Two fire rangers in watch towers that are 10 miles apart spotted a fire at the same time. The first ranger indicated that the position of the fire made an angle of 39° with the line between the towers. The second ranger indicated that it made an angle of 34° with the same line. How far is the second tower from the fire?
- 6.6 mi (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
- 5.8 mi (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
- 10 mi (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
- 12.4 mi (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
A: 6.6 mi

Q: After flying at an altitude of 500 meters, a hang glider starts to descend when the ground distance from the landing pad is 15 kilometers. What is the angle of depression for this part of the flight?
- 1.7° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 1.9° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 88.1° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 88.3° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 1.9°

Q: Find each measure using the given measures of [Image]. Round angle measures to the nearest degree and side measures to the nearest tenth.

If [Image] 47.1, [Image] 59.6, and [Image] 52.2, find [Image].
- 45.8 (Substitute the given values into the Law of Sines. Cross multiply. Divide each side by the length of side l.)
- 0.8 (Substitute the given values into the Law of Sines. Cross multiply. Divide each side by the length of side l.)
- 56.7 (Substitute the given values into the Law of Sines. Cross multiply. Divide each side by the length of side l.)
- 43.6 (Substitute the given values into the Law of Sines. Cross multiply. Divide each side by the length of side l.)
A: 56.7

Q: After flying at an altitude of 600 meters, a hot air balloon starts to descend when its ground distance from the landing pad is 10 kilometers. What is the angle of depression for this part of the flight?
- 0.95° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 3.43° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 86.57° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 89.05° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 3.43°

Q: David and his friends are building a fort on a triangular plot of land. They want to dig a moat around the fort. The length of one side of the plot of land is 27 feet. If the angles at the end of this side are 45° and 75°, find the length of the moat that will enclose the entire plot of land on which the fort is built.
- 22.0 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing sides. Find the perimeter.)
- 30.1 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing sides. Find the perimeter.)
- 60 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing sides. Find the perimeter.)
- 79.1 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing sides. Find the perimeter.)
A: 79.1 ft

Q: A water slide is 400 yards long with a vertical drop of 36.3 yards. Find the angle of depression of the slide.
- 5.2° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 84.8° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 436.3° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 363.7° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 5.2°

Q: Members of the soccer team are trying to map out some new plays before their next game. The goal is 24 feet wide.

Sophie’s favorite play has a player standing 18 feet from one goal post and 21 feet from the other post. What is the angle to make a shot on goal?
- 43.4 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 46.6 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 57.9 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 75.5 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
A: 75.5

Q: Find each measure using the given measures of [Image]. Round angle measures to the nearest degree and side measures to the nearest tenth.

If [Image] 48.4, [Image] 24.5, and [Image] 37.9, find k.
- 15.7 (Substitute the given values into the Law of Sines. Cross multiply. Divide each side by [Image].)
- 21.0 (Substitute the given values into the Law of Sines. Cross multiply. Divide each side by [Image].)
- 28.3 (Substitute the given values into the Law of Sines. Cross multiply. Divide each side by [Image].)
- 68.3 (Substitute the given values into the Law of Sines. Cross multiply. Divide each side by [Image].)
A: 21.0

Q: Kim’s route from her front door to the mailbox, the swing set, and back to the front door forms a triangle. Two legs of the triangle are 245 feet long and they meet at an angle of 38°. How long is the entire route?
- 142 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing side. Find the perimeter.)
- 159.5 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing side. Find the perimeter.)
- 404.5 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing side. Find the perimeter.)
- 649.5 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing side. Find the perimeter.)
A: 649.5 ft

Q: After traveling steadily at 400 meters above a shipwrecked hull, a submerged vessel starts to descend when its ground distance from the hull is 7 kilometers. What is the angle of depression for this part of the travel?
- 1.00° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 3.27° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 86.73° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 88.00° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 3.27°

Q: Hoshi is working on an art project in the shape of a triangular prism. The sides of the triangle are 2.4 feet, 1.5 feet, and 1.3 feet. Find the measures of the angles of the triangle to the nearest tenth.
- 117.8, 33.6, 28.6 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 27.8, 56.4, 95.8 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 25.0, 39.8, 115.2 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 60, 60, 60 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
A: 117.8, 33.6, 28.6

Q: Taina, Luther, and Della are tapping a balloon to each other in the air, trying to keep it from touching the ground. The distance from Taina to Luther is 22 inches. The distance from Luther to Della is 40 inches. The distance from Della to Taina is 34 inches. Find the measures of the three angles in the triangle.
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- [Image], [Image], [Image] (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
A: [Image], [Image], [Image]

Q: A ski slope is 250 yards long with a vertical drop of 100 yards. Find the angle of depression of the slope.
- 21.8° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 23.6° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 66.4° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 68.2° (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 23.6°

Q: Two lifeguards at the lake are stationed 28 meters apart. They both located a struggling swimmer at the same time. The first lifeguard indicated that the position of the swimmer made an angle of 50° with the line between the lifeguard chairs. The second lifeguard indicated that the swimmer made an angle of 56° with the same line. How far is the first lifeguard from the swimmer?
- 24.1 m (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
- 22.3 m (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
- 28 m (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
- 74 m (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
A: 24.1 m

Q: Members of the soccer team are trying to map out some new plays before their next game. The goal is 24 feet wide.

Pedro came up with a play that would put him 35 feet from one goal post and 45 feet from the other post. What is his angle to make a shot on goal?
- 31.9 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 48.4 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 100.8 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 180 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
A: 31.9

Q: Lin is planning a triangular dog run. He wants to build a fence around the run. The length of one side of the dog run is 38 feet. If the angles at the end of this side are 48° and 82°, find the length of fence needed to enclose the dog run.
- 36.9 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing sides. Find the perimeter.)
- 49.1 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing sides. Find the perimeter.)
- 50 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing sides. Find the perimeter.)
- 124 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing sides. Find the perimeter.)
A: 124 ft

Q: Maria is erecting a statue on a triangular plot of land. She wants to put decorative stonework edging around the site. The length of one side of the plot of land is 25 feet. If the angles at the end of this side are 65° and 38°, find the length of stonework edging needed to enclose the site on which the statue is erected.
- 15.8 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing sides. Find the perimeter.)
- 23.3 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing sides. Find the perimeter.)
- 64.1 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing sides. Find the perimeter.)
- 77 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing sides. Find the perimeter.)
A: 64.1 ft

Q: Two observation stations that are 15 miles apart located a ship at the same time. The first station indicated that the position of the ship made an angle of 38° with the line between the stations. The second station indicated that it made an angle of 36° with the same line. How far is the first station from the ship?
- 9.17 mi (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
- 9.6 mi (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
- 15 mi (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
- 18.77 mi (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the requested side.)
A: 9.17 mi

Q: A horse corral is situated on a triangular plot of land. Two sides of the plot are 150 feet long and they meet at an angle of 55°. A fence is to be placed along the perimeter of the corral. How much fencing material is needed?
- 125 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing side. Find the perimeter.)
- 138.5 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing side. Find the perimeter.)
- 288.5 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing side. Find the perimeter.)
- 438.5 ft (Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the missing side. Find the perimeter.)
A: 438.5 ft

Q: Two swimmers are observed by a lifeguard in a 30 feet tower above the water. The angles of depression are 12.7° and 14.5°. How far apart are the swimmers?
- 249.1 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 133.1 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 116.0 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
- 17.1 ft (Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer.)
A: 17.1 ft

Q: In [Image], given the lengths of the sides, find the measure of the stated angle to the nearest degree.
[Image], [Image], [Image]; [Image]
- 0.20 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 102 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- –2.3 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 78 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
A: 78

Q: Luna created a trash can in the shape of a triangular prism. The sides of the triangle are 1.6 feet, 2.3 feet, and 1.2 feet. Find the measures of the angles of the triangle to the nearest tenth.
- 109.6, 41.0, 29.4 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 19.6, 49.1, 60.6 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 101.8, 37.1, 41.1 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
- 60, 60, 60 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated angle by using inverse cosine.)
A: 109.6, 41.0, 29.4

Q: In [Image], given the following measures, find the measure of the missing side.
[Image], [Image], [Image]
- b » 6.7 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the square root of both sides.)
- b » 394 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the square root of both sides.)
- b » 14.5 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the square root of both sides.)
- b » 45.3 (Substitute the given values into the Law of Cosines. Simplify the equation. Find the square root of both sides.)
A: b » 6.7

Carla, Dani, and Ellis are practicing with a giant slingshot. Carla is standing at point C and Dani is standing at point D. Each of them is holding the handle for one end of the slingshot. Ellis is pulling back the middle of the slingshot, from which a ball will be released. Ellis is standing at point E, equidistant from Carla and Dani. When Ellis releases the ball from the slingshot, it will travel through point K. Prove that when Ellis’s ball goes through point K, it will be at the midpoint between Carla and Dani.
[Image]

Alvin, Ben, and Carmen are practicing for a marathon. Alvin is standing at point A and Ben is standing at point B, and each is holding an end of the finish line tape. Carmen is standing at C, equidistant from Alvin and Ben. Carmen will run through the middle of the tape at point K. Prove that when Carmen runs through the tape, she will be at the midpoint between Alvin and Ben.
[Image]