Trigonometry Study Resources for Competitive Exams

Trigonometry

Heights & Distances Properties of Triangles Trigonometric Equations Trigonometric Ratios & Identities

Q. A building is 30 meters tall. From a point 40 meters away from the base of the building, what is the angle of elevation to the top of the building?

A. 30 degrees
B. 36.87 degrees
C. 45 degrees
D. 60 degrees

Solution

Using tan(θ) = height/distance, we have tan(θ) = 30/40 = 0.75. Therefore, θ = tan⁻¹(0.75) ≈ 36.87 degrees.

Correct Answer: B — 36.87 degrees

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Q. A building is 40 m high. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. What is the distance from the point to the base of the building?

A. 20√3 m
B. 40 m
C. 30 m
D. 10√3 m

Solution

Using tan(60°) = height/distance, we have distance = height/tan(60°) = 40/√3 = 20√3 m.

Correct Answer: A — 20√3 m

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Q. A building is 40 meters tall. From a point 30 meters away from the base of the building, what is the angle of elevation to the top of the building?

A. 30 degrees
B. 36.87 degrees
C. 45 degrees
D. 53.13 degrees

Solution

Using tan(θ) = height/distance, we have tan(θ) = 40/30. Therefore, θ = tan⁻¹(4/3) ≈ 53.13 degrees.

Correct Answer: B — 36.87 degrees

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Q. A building is 50 meters tall. From a point 40 meters away from the base of the building, what is the angle of elevation to the top of the building?

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 75 degrees

Solution

Using tan(θ) = height/distance, we have θ = tan^(-1)(50/40) = tan^(-1)(1.25) which is approximately 60 degrees.

Correct Answer: C — 60 degrees

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Q. A kite is flying at a height of 100 m. If the angle of elevation from a point on the ground to the kite is 30 degrees, how far is the point from the base of the kite?

A. 100 m
B. 200 m
C. 300 m
D. 400 m

Solution

Using tan(30°) = height/distance, we have 1/√3 = 100/distance. Therefore, distance = 100√3 ≈ 173.2 m.

Correct Answer: B — 200 m

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Q. A kite is flying at a height of 100 meters. If the angle of depression from the kite to a point on the ground is 30 degrees, how far is the point from the point directly below the kite?

A. 50 m
B. 60 m
C. 70 m
D. 80 m

Solution

Using tan(30°) = 100/distance, we have 1/√3 = 100/distance. Therefore, distance = 100√3 ≈ 173.21 m.

Correct Answer: A — 50 m

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Q. A kite is flying at a height of 30 m. If the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite?

A. 15√3 m
B. 30 m
C. 10√3 m
D. 20 m

Solution

Using tan(60°) = height/distance, we have distance = height/tan(60°) = 30/√3 = 15√3 m.

Correct Answer: A — 15√3 m

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Q. A kite is flying at a height of 30 meters. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite?

A. 15 m
B. 30 m
C. 45 m
D. 60 m

Solution

Using tan(45°) = height/distance, we have 1 = 30/distance. Therefore, distance = 30 m.

Correct Answer: B — 30 m

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Q. A kite is flying at a height of 50 meters. If the angle of elevation from a point on the ground to the kite is 30 degrees, how far is the point from the base of the kite?

A. 50√3 meters
B. 25√3 meters
C. 100 meters
D. 75 meters

Solution

Distance = height / tan(angle) = 50 / (1/√3) = 50√3 meters.

Correct Answer: B — 25√3 meters

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Q. A ladder 10 m long reaches a window 8 m above the ground. What is the angle of elevation of the ladder from the ground?

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 75 degrees

Solution

Using sin(θ) = opposite/hypotenuse, we have sin(θ) = 8/10. Therefore, θ = sin⁻¹(0.8) ≈ 53.13 degrees.

Correct Answer: C — 60 degrees

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Q. A ladder 15 meters long reaches a window 12 meters above the ground. What is the angle of elevation of the ladder from the ground?

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 75 degrees

Solution

Using sin(θ) = opposite/hypotenuse, we have sin(θ) = 12/15. Therefore, θ = sin⁻¹(0.8) ≈ 53.13 degrees.

Correct Answer: C — 60 degrees

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Q. A ladder is leaning against a wall. The foot of the ladder is 12 meters away from the wall, and the angle between the ladder and the ground is 60 degrees. What is the height at which the ladder touches the wall?

A. 12√3 m
B. 6 m
C. 12 m
D. 24 m

Solution

Using sin(60°) = height/hypotenuse, we find the height = 12 * tan(60°) = 12√3 m.

Correct Answer: A — 12√3 m

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Q. A man 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 man is standing 30 meters away from a tower. If the angle of elevation of the top of the tower from the man's position is 30 degrees, what is the height of the tower?

A. 15√3 meters
B. 30 meters
C. 15 meters
D. 10√3 meters

Solution

Height = distance * tan(angle) = 30 * tan(30°) = 30 * (1/√3) = 10√3 meters.

Correct Answer: A — 15√3 meters

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Q. A man is standing 30 meters away from a tree. If the angle of elevation from his eyes to the top of the tree is 30 degrees, what is the height of the tree?

A. 15√3 meters
B. 15 meters
C. 30 meters
D. 45 meters

Solution

Height = distance * tan(angle) = 30 * tan(30°) = 30 * (1/√3) = 10√3 meters.

Correct Answer: A — 15√3 meters

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Q. A man is standing 50 meters away from a vertical pole. If he looks up at an angle of elevation of 60 degrees to the top of the pole, 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 man is standing on a hill 80 meters high. If he looks at a point on the ground at an angle of depression of 45 degrees, how far is the point from the base of the hill?

A. 80 meters
B. 40√2 meters
C. 80√2 meters
D. 60 meters

Solution

Distance = height / tan(angle) = 80 / tan(45°) = 80 meters.

Correct Answer: A — 80 meters

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Q. A man is standing on a hill that is 80 m high. If he looks down at an angle of depression of 30 degrees, how far is he from the base of the hill?

A. 40 m
B. 60 m
C. 80 m
D. 100 m

Solution

Using tan(30°) = height/distance, we have 1/√3 = 80/distance. Therefore, distance = 80√3 ≈ 138.56 m.

Correct Answer: A — 40 m

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Q. A man is standing on the ground and looking at the top of a 15 m high pole. If he is 20 m away from the base of the pole, what is the angle of elevation?

A. 36.87 degrees
B. 45 degrees
C. 60 degrees
D. 30 degrees

Solution

Using tan(θ) = height/distance, we have tan(θ) = 15/20. Therefore, θ = tan⁻¹(0.75) which is approximately 36.87 degrees.

Correct Answer: A — 36.87 degrees

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Q. A man is standing on the ground and looking at the top of a building. If the angle of elevation is 45 degrees and he is 10 meters away from the building, what is the height of the building?

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

Solution

Height = distance * tan(angle) = 10 * tan(45°) = 10 meters.

Correct Answer: A — 10 meters

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Q. A man is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and he is 10 meters away from the base of the tree, what is the height of the tree?

A. 5√3 m
B. 10√3 m
C. 15√3 m
D. 20√3 m

Solution

Using tan(60°) = height/10, we have √3 = height/10. Therefore, height = 10√3 m.

Correct Answer: B — 10√3 m

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Q. A man is standing on the ground and observes the top of a building at an angle of elevation of 60 degrees. If he is 50 m away from the building, what is the height of the building?

A. 25 m
B. 43.3 m
C. 50 m
D. 86.6 m

Solution

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

Correct Answer: B — 43.3 m

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Q. A man is standing on the ground and observes the top of a tree at an angle of elevation of 45 degrees. If he 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 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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