Heights & Distances Study Guide for Competitive Exams

Heights & Distances

Q. A person is standing 20 meters away from a vertical cliff. If the angle of elevation to the top of the cliff is 60 degrees, what is the height of the cliff?

A. 10√3 m
B. 20√3 m
C. 30√3 m
D. 40√3 m

Solution

Using tan(60°) = height/20, we have √3 = height/20. Therefore, height = 20√3 m.

Correct Answer: B — 20√3 m

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Q. A person is standing 25 meters away from a vertical cliff. If the angle of elevation to the top of the cliff is 60 degrees, what is the height of the cliff?

A. 10 m
B. 15 m
C. 20 m
D. 25 m

Solution

Using tan(60°) = height/25, we have √3 = height/25. Therefore, height = 25√3 ≈ 43.3 m.

Correct Answer: C — 20 m

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Q. A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 36.87 degrees, what is the height of the pole?

A. 15 m
B. 20 m
C. 25 m
D. 30 m

Solution

Using tan(36.87°) = height/distance, we have height = distance * tan(36.87°) = 25 * 0.75 = 15 m.

Correct Answer: A — 15 m

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Q. A person is standing 30 m away from the base of a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?

A. 15 m
B. 20 m
C. 25 m
D. 30 m

Solution

Using tan(60°) = height/30, we have √3 = height/30. Therefore, height = 30√3 = 25 m.

Correct Answer: C — 25 m

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Q. A person is standing 30 m away from the foot of a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?

A. 15 m
B. 20 m
C. 25 m
D. 30 m

Solution

Using tan(60°) = height/30, we have √3 = height/30. Therefore, height = 30√3 = 25 m.

Correct Answer: C — 25 m

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Q. A person is standing 30 meters away from the foot of a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?

A. 15√3 m
B. 30 m
C. 30√3 m
D. 45 m

Solution

Using tan(60°) = height/distance, we have height = distance * tan(60°) = 30√3 m.

Correct Answer: A — 15√3 m

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Q. A person is standing 40 m away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?

A. 20√3 m
B. 40 m
C. 30 m
D. 50 m

Solution

Using tan(60°) = height/40, we have √3 = height/40. Therefore, height = 40√3 m.

Correct Answer: A — 20√3 m

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Q. A person is standing 40 m away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?

A. 20 m
B. 40 m
C. 30 m
D. 10 m

Solution

Using tan(30°) = height/distance, we have height = distance * tan(30°) = 40 * (1/√3) ≈ 20 m.

Correct Answer: A — 20 m

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Q. A person is standing 50 m away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?

A. 25√3 m
B. 50 m
C. 30 m
D. 40 m

Solution

Using tan(30°) = height/50, we have 1/√3 = height/50. Therefore, height = 50/√3 m.

Correct Answer: A — 25√3 m

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Q. A person is standing 50 meters away from a vertical pole. If the angle of elevation of the top of the pole is 60 degrees, what is the height of the pole?

A. 25 m
B. 30 m
C. 35 m
D. 40 m

Solution

Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.

Correct Answer: B — 30 m

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Q. A person is standing 50 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?

A. 25 m
B. 30 m
C. 35 m
D. 40 m

Solution

Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.

Correct Answer: B — 30 m

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Q. A person is standing at a distance of 20 m from a vertical pole. If the angle of elevation to the top of the pole is 45 degrees, what is the height of the pole?

A. 20 m
B. 10 m
C. 30 m
D. 15 m

Solution

Using tan(45°) = height/distance, we have height = distance * tan(45°) = 20 * 1 = 20 m.

Correct Answer: A — 20 m

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Q. A person is standing at a distance of 40 m from a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?

A. 20√3 m
B. 40 m
C. 30 m
D. 10√3 m

Solution

Using tan(60°) = height/distance, we have height = distance * tan(60°) = 40√3 m.

Correct Answer: A — 20√3 m

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Q. A person is standing at a distance of 40 meters from the base of a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?

A. 20 m
B. 30 m
C. 40 m
D. 50 m

Solution

Using tan(60°) = height/40, we have √3 = height/40. Therefore, height = 40√3 ≈ 69.28 m.

Correct Answer: C — 40 m

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Q. A person is standing on a hill 100 meters high. If he looks at a point on the ground at an angle of depression of 30 degrees, how far is the point from the base of the hill?

A. 100√3 meters
B. 100 meters
C. 50√3 meters
D. 50 meters

Solution

Distance = height / tan(angle) = 100 / tan(30°) = 100√3 meters.

Correct Answer: A — 100√3 meters

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Q. A person is standing on a hill 80 m high. The angle of depression to a car on the ground is 60 degrees. How far is the car from the base of the hill?

A. 40 m
B. 80 m
C. 20√3 m
D. 40√3 m

Solution

Using tan(60°) = height/distance, we have distance = height/tan(60°) = 80/√3 = 40√3 m.

Correct Answer: D — 40√3 m

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Q. A person is standing on a hill that is 80 meters high. If the angle of depression to a point on the ground is 45 degrees, how far is the point from the base of the hill?

A. 80 m
B. 40 m
C. 80√2 m
D. 40√2 m

Solution

Using tan(45°) = height/distance, we have distance = height/tan(45°) = 80/1 = 80 m.

Correct Answer: A — 80 m

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Q. A person is standing on the ground and looking at the top of a building. If the angle of elevation is 45 degrees and the person is 20 meters away from the building, what is the height of the building?

A. 20 meters
B. 10 meters
C. 30 meters
D. 25 meters

Solution

Height = distance * tan(angle) = 20 * 1 = 20 meters.

Correct Answer: A — 20 meters

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Q. A person is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and the person is 20 meters away from the tree, what is the height of the tree?

A. 20√3 meters
B. 10√3 meters
C. 30 meters
D. 40 meters

Solution

Height = distance * tan(angle) = 20 * tan(60°) = 20 * √3 meters.

Correct Answer: A — 20√3 meters

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Q. A person standing 20 meters away from a vertical cliff observes the top of the cliff at an angle of elevation of 75 degrees. What is the height of the cliff?

A. 10 m
B. 15 m
C. 20 m
D. 25 m

Solution

Using tan(75°) = height/20, we have height = 20 * tan(75°) ≈ 20 * 3.732 = 74.64 m.

Correct Answer: D — 25 m

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Q. A person standing 40 m away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?

A. 10 m
B. 20 m
C. 30 m
D. 40 m

Solution

Using tan(30°) = height/40, we have 1/√3 = height/40. Therefore, height = 40/√3 ≈ 23.1 m.

Correct Answer: B — 20 m

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Q. A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building?

A. 40√3 meters
B. 20√3 meters
C. 30 meters
D. 50 meters

Solution

Height = distance * tan(angle) = 40 * tan(60°) = 40√3 meters.

Correct Answer: A — 40√3 meters

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Q. A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?

A. 20 m
B. 40 m
C. 30 m
D. 10 m

Solution

Height = distance * tan(angle) = 40 * 1 = 40 m.

Correct Answer: B — 40 m

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Q. A person standing 50 m away from a building observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building?

A. 25 m
B. 30 m
C. 35 m
D. 40 m

Solution

Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.

Correct Answer: B — 30 m

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Q. A person standing 50 m away from a tree observes the angle of elevation to the top of the tree as 30 degrees. What is the height of the tree?

A. 25 m
B. 50 m
C. 15 m
D. 20 m

Solution

Using tan(30°) = height/distance, we have height = distance * tan(30°) = 50 * (1/√3) = 25 m.

Correct Answer: A — 25 m

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Q. A person standing 50 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?

A. 25 meters
B. 50 meters
C. 35 meters
D. 45 meters

Solution

Height = distance * tan(angle) = 50 * tan(45°) = 50 meters.

Correct Answer: B — 50 meters

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Q. A person standing 60 meters away from a tree sees the top of the tree at an angle of elevation of 30 degrees. What is the height of the tree?

A. 20√3 m
B. 30 m
C. 60 m
D. 10 m

Solution

Height = distance * tan(angle) = 60 * (1/√3) = 20√3 m.

Correct Answer: A — 20√3 m

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Q. A person standing on the ground observes the top of a tree at an angle of elevation of 45 degrees. If the person is 10 meters away from the tree, what is the height of the tree?

A. 5 m
B. 10 m
C. 15 m
D. 20 m

Solution

Using tan(45°) = height/10, we have 1 = height/10. Therefore, height = 10 m.

Correct Answer: B — 10 m

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Q. A tower is 100 meters high. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. How far is the point from the base of the tower?

A. 100√3 meters
B. 50√3 meters
C. 200 meters
D. 150 meters

Solution

Distance = height / tan(angle) = 100 / (1/√3) = 100√3 meters.

Correct Answer: A — 100√3 meters

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Q. A tower is 40 meters high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower?

A. 20√3 meters
B. 40 meters
C. 20 meters
D. 30 meters

Solution

Distance = height / tan(angle) = 40 / tan(60°) = 40 / √3 = 20√3 meters.

Correct Answer: A — 20√3 meters

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Heights & Distances

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