Height and Distance: Mastering Concepts for Competitive Exams

Height and Distance

Q. A person is standing 50 meters away from a cliff. If the angle of elevation to the top of the cliff is 30°, what is the height of the cliff?

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

Solution

Height = distance * tan(30°) = 50 * (1/√3) = 25 meters.

Correct Answer: A — 25 meters

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Q. A person is standing 50 meters away from a hill. If the angle of elevation to the top of the hill is 37 degrees, what is the height of the hill?

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

Solution

Height = distance * tan(angle) = 50 * tan(37°) ≈ 30 meters.

Correct Answer: A — 30 meters

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

A. 25√3 meters
B. 50 meters
C. 30 meters
D. 40 meters

Solution

Height = distance * tan(angle) = 50 * (1/√3) = 50/√3 = 25√3 meters.

Correct Answer: A — 25√3 meters

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Q. A person is standing 50 meters away from a statue. If the angle of elevation to the top of the statue is 45 degrees, what is the height of the statue?

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

Solution

Height = distance * tan(angle) = 50 * 1 = 50 meters.

Correct Answer: B — 50 meters

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Q. A person looks at the top of a building from a distance of 50 meters. If the angle of elevation is 30 degrees, what is the height of the building?

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

Solution

Height = distance * tan(30) = 50 * (1/√3) ≈ 25 meters.

Correct Answer: A — 25 meters

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Q. A person looks at the top of a tree from a distance of 40 meters. If the angle of elevation is 30 degrees, what is the height of the tree?

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

Solution

Height = distance * tan(angle) = 40 * (1/√3) ≈ 20 meters.

Correct Answer: A — 20 meters

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Q. A person standing 100 meters away from a hill observes the top of the hill at an angle of elevation of 60 degrees. What is the height of the hill?

A. 100√3
B. 50√3
C. 75√3
D. 25√3

Solution

height = distance * tan(60) = 100 * √3 = 100√3 meters

Correct Answer: A — 100√3

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Q. A person standing 15 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. 10 m
B. 15 m
C. 20 m
D. 30 m

Solution

Height = distance * tan(45) = 15 * 1 = 15 m

Correct Answer: B — 15 m

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Q. A person standing 15 meters away from a statue sees the top of the statue at an angle of elevation of 45 degrees. What is the height of the statue?

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

Solution

Using tan(45) = height/distance, height = distance * tan(45) = 15 * 1 = 15 meters.

Correct Answer: A — 15 meters

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Q. A person standing 20 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 meters
B. 10 meters
C. 30 meters
D. 15 meters

Solution

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

Correct Answer: A — 20 meters

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Q. A person standing 20 meters away from a wall sees the top of the wall at an angle of elevation of 30 degrees. What is the height of the wall?

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

Solution

Height = distance * tan(angle) = 20 * (1/√3) = 20 / 1.732 = 11.55 meters.

Correct Answer: B — 10 meters

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Q. A person standing 25 meters away from a building observes the top of the building at an angle of elevation of 53 degrees. What is the height of the building?

A. 15 meters
B. 20 meters
C. 30 meters
D. 40 meters

Solution

Height = distance * tan(angle) = 25 * tan(53) ≈ 25 * 1.327 = 33.175 meters.

Correct Answer: C — 30 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 30 degrees. What is the height of the building?

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

Solution

Height = distance * tan(angle) = 40 * (1/√3) = 40/√3 = 10√3 meters.

Correct Answer: B — 10√3 meters

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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 30 degrees. What is the height of the building?

A. 25 meters
B. 15√3 meters
C. 10√3 meters
D. 20 meters

Solution

Height = distance * tan(30) = 50 * (1/√3) = 50/√3 = 15√3 meters

Correct Answer: B — 15√3 meters

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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 60 degrees. What is the height of the building?

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

Solution

Height = distance * tan(angle) = 50 * √3 = 25√3 meters.

Correct Answer: A — 25√3 meters

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Q. A tower is 100 meters high. From a point 80 meters away from the base of the tower, what is the angle of elevation to the top of the tower?

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

Solution

tan(θ) = height/distance = 100/80, θ = tan⁻¹(1.25) ≈ 51.34 degrees.

Correct Answer: B — 60 degrees

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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 45 degrees. How far is the point from the base of the tower?

A. 50 meters
B. 100 meters
C. 75 meters
D. 125 meters

Solution

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

Correct Answer: B — 100 meters

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Q. A tower is 50 meters high. From a point 30 meters away from the base of the tower, what is the angle of elevation to the top of the tower?

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

Solution

tan(θ) = height / distance = 50 / 30; θ = tan^(-1)(5/3) ≈ 60 degrees

Correct Answer: C — 60 degrees

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

A. 36.87 degrees
B. 45 degrees
C. 53.13 degrees
D. 60 degrees

Solution

tan(θ) = height/distance = 50/40, θ = tan⁻¹(1.25) ≈ 51.34 degrees.

Correct Answer: A — 36.87 degrees

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Q. A tower is 50 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower?

A. 25 meters
B. 35 meters
C. 50 meters
D. 70 meters

Solution

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

Correct Answer: C — 50 meters

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Q. A tree casts a shadow of 10 meters long. If the angle of elevation of the sun is 30 degrees, what is the height of the tree?

A. 5√3 meters
B. 10 meters
C. 10√3 meters
D. 15 meters

Solution

Height = shadow * tan(angle) = 10 * √3 = 5√3 meters.

Correct Answer: A — 5√3 meters

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Q. A tree casts a shadow of 10 meters when the angle of elevation of the sun is 30 degrees. What is the height of the tree?

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

Solution

Height = shadow * tan(angle) = 10 * √3 = 10 * 1.732 = 17.32 meters.

Correct Answer: C — 15 meters

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Q. A tree casts a shadow of 10 meters when the angle of elevation of the sun is 45 degrees. What is the height of the tree?

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

Solution

Height = shadow * tan(45) = 10 * 1 = 10 meters.

Correct Answer: A — 10 meters

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Q. A tree is 10 meters tall. From a point 20 meters away from the base of the tree, the angle of elevation to the top of the tree is what?

A. 26.57 degrees
B. 30 degrees
C. 36.87 degrees
D. 45 degrees

Solution

tan(θ) = height/distance = 10/20 => θ = tan⁻¹(0.5) = 26.57 degrees

Correct Answer: C — 36.87 degrees

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Q. A tree is 15 meters tall. From a point 20 meters away from the base of the tree, what is the angle of elevation to the top of the tree?

A. 36.87 degrees
B. 45 degrees
C. 53.13 degrees
D. 60 degrees

Solution

tan(θ) = height/distance = 15/20; θ = tan⁻¹(15/20) = 36.87 degrees.

Correct Answer: C — 53.13 degrees

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Q. A tree is 15 meters tall. If the angle of elevation from a point 20 meters away from the base of the tree is θ, what is tan(θ)?

A. 0.75
B. 1.25
C. 1.5
D. 2

Solution

tan(θ) = height / distance = 15 / 20 = 0.75

Correct Answer: A — 0.75

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Q. A tree is 15 meters tall. If the angle of elevation from a point on the ground 20 meters away from the base of the tree is θ, what is tan(θ)?

A. 0.75
B. 0.6
C. 0.5
D. 0.8

Solution

tan(θ) = height/base = 15/20 = 0.75.

Correct Answer: A — 0.75

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Q. A tree is 15 meters tall. If the angle of elevation from a point on the ground to the top of the tree is 30 degrees, how far is the point from the base of the tree?

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

Solution

Using tan(30) = height/distance, distance = height/tan(30) = 15/√3 meters.

Correct Answer: B — 15/√3 meters

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Q. A tree is 30 meters tall. If the angle of elevation from a point 40 meters away from the base of the tree is θ, what is tan(θ)?

A. 0.75
B. 0.6
C. 0.5
D. 0.8

Solution

tan(θ) = height / distance = 30 / 40 = 0.75

Correct Answer: A — 0.75

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Q. From a point 15 meters away from the base of a hill, the angle of elevation to the top of the hill is 60°. What is the height of the hill?

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

Solution

Using tan(60°) = height/15, height = 15 * √3 = 25.98 meters, approximately 26 meters.

Correct Answer: C — 20 meters

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Height and Distance

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