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Q. A person is running at 3 m/s on a moving escalator that moves at 2 m/s in the same direction. What is the speed of the person relative to a stationary observer?

A. 1 m/s
B. 3 m/s
C. 5 m/s
D. 2 m/s

Solution

Speed of person relative to observer = Speed of escalator + Speed of person = 2 m/s + 3 m/s = 5 m/s.

Correct Answer: C — 5 m/s

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Q. A person is running at 8 m/s in a train moving at 12 m/s in the same direction. What is the speed of the person relative to the ground?

A. 4 m/s
B. 8 m/s
C. 12 m/s
D. 20 m/s

Solution

Speed of person relative to ground = Speed of train + Speed of person = 12 m/s + 8 m/s = 20 m/s.

Correct Answer: D — 20 m/s

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Q. A person is running at 8 m/s on a moving walkway that moves at 2 m/s in the same direction. What is the speed of the person relative to the ground?

A. 6 m/s
B. 8 m/s
C. 10 m/s
D. 12 m/s

Solution

Speed relative to ground = Speed of person + Speed of walkway = 8 m/s + 2 m/s = 10 m/s.

Correct Answer: C — 10 m/s

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Q. A person is running at a speed of 10 m/s. If he is running towards a train moving at 20 m/s in the opposite direction, what is the relative speed of the train with respect to the person?

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

Solution

Relative speed = speed of train + speed of person = 20 + 10 = 30 m/s.

Correct Answer: C — 30 m/s

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Q. A person is standing 100 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?

A. 100 m
B. 50 m
C. 75 m
D. 25 m

Solution

Using tan(45°) = height/distance, we have height = distance * tan(45°) = 100 * 1 = 100 m.

Correct Answer: A — 100 m

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Q. A person is standing 20 m away from a building and sees the top of the building at an angle of elevation of 45 degrees. What is the height of the building? (2019)

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

Solution

Height = distance * tan(angle) = 20 * tan(45) = 20 * 1 = 20 m.

Correct Answer: B — 20 m

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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 a tree and observes the top of the tree at an angle of elevation of 60 degrees. What is the height of the tree? (2022)

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

Solution

Height = distance * tan(angle) = 30 * tan(60) = 30 * √3 ≈ 25 m.

Correct Answer: C — 25 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 and observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building? (2023)

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

Solution

Height = distance * tan(60) = 40 * √3 ≈ 69.28 m, which rounds to 50 m.

Correct Answer: D — 50 m

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Q. A person is standing 40 m away from a building and sees the top of the building at an angle of elevation of 45 degrees. What is the height of the building? (2020)

A. 20 m
B. 30 m
C. 40 m
D. 45 m

Solution

Height = distance * tan(45) = 40 * 1 = 40 m.

Correct Answer: C — 40 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 is walking at 2 m/s on a train moving at 10 m/s. What is the speed of the person relative to the ground?

A. 2 m/s
B. 8 m/s
C. 10 m/s
D. 12 m/s

Solution

Speed of person relative to ground = Speed of train + Speed of person = 10 m/s + 2 m/s = 12 m/s.

Correct Answer: D — 12 m/s

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Q. A person is walking at 4 km/h in a train moving at 36 km/h. What is the speed of the person relative to the ground?

A. 32 km/h
B. 40 km/h
C. 36 km/h
D. 4 km/h

Solution

Speed of person relative to ground = Speed of train + Speed of person = 36 km/h + 4 km/h = 40 km/h.

Correct Answer: B — 40 km/h

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Major Competitive Exams

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