Height and Distance: Mastering Concepts for Competitive Exams

Height and Distance

Q. A ladder leans against a wall making an angle of 60 degrees with the ground. If the foot of the ladder is 5 meters away from the wall, what is the height of the ladder on the wall?

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

Solution

Height = 5 * √3 = 5√3 meters.

Correct Answer: A — 5√3 meters

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Q. A man is 50 meters away from a building. If he looks up at an angle of 60 degrees to see the top of the building, what is the height of the building?

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

Solution

Height = distance * tan(angle) = 50 * √3 = 50 * 1.732 = 86.6 meters.

Correct Answer: D — 40 meters

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Q. A man is 50 meters away from a tower. If he looks at the top of the tower at an angle of elevation of 45 degrees, what is the height of the tower?

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

Solution

Height = distance * tan(45) = 50 * 1 = 50 meters.

Correct Answer: A — 50 meters

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Q. A man is standing 12 meters away from a vertical pole. If he looks up at an angle of 30 degrees to see the top of the pole, what is the height of the pole?

A. 6 meters
B. 12 meters
C. 8 meters
D. 10 meters

Solution

Height = distance * tan(30) = 12 * (1/√3) = 12/√3 = 4√3 meters.

Correct Answer: A — 6 meters

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Q. A man is standing 15 meters away from a wall. If he looks up at an angle of 30 degrees to see the top of the wall, what is the height of the wall?

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

Solution

Height = distance * tan(angle) = 15 * (1/√3) ≈ 15 * 0.577 = 8.66 meters.

Correct Answer: B — 10 meters

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Q. A man is standing 25 meters away from a vertical pole. If he looks up at an angle of 45 degrees, what is the height of the pole?

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

Solution

Height = distance * tan(angle) = 25 * 1 = 25 meters.

Correct Answer: A — 25 meters

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Q. A man is standing 30 meters 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. 15√3 meters
B. 30√3 meters
C. 45 meters
D. 60 meters

Solution

Height = distance * tan(60) = 30 * √3 = 15√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 60 degrees, what is the height of the tree?

A. 15 meters
B. 25 meters
C. 30 meters
D. 35 meters

Solution

Height = distance * tan(angle) = 30 * √3 = 30 * 1.732 = 51.96 meters.

Correct Answer: B — 25 meters

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Q. A man is standing 40 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. 40 meters
B. 20 meters
C. 30 meters
D. 50 meters

Solution

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

Correct Answer: A — 40 meters

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Q. A man is standing 50 meters 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
B. 15√3
C. 20√3
D. 10√3

Solution

height = distance * tan(30) = 50 * (1/√3) = 50/√3 = 25√3 meters

Correct Answer: A — 25√3

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Q. A man is standing 50 meters 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. 25 meters
B. 30 meters
C. 35 meters
D. 40 meters

Solution

Height = distance * tan(angle) = 50 * √3 = 50 * 1.732 = 86.6 meters.

Correct Answer: D — 40 meters

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Q. A person is looking at the top of a 40-meter tall building from a distance of 50 meters. What is the angle of elevation?

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

Solution

tan(θ) = height/distance = 40/50, θ = tan⁻¹(0.8) ≈ 38.66 degrees.

Correct Answer: B — 36.87 degrees

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

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

Solution

Height = distance * tan(30) = 50 * (1/√3) = 50/√3 ≈ 28.87 meters.

Correct Answer: A — 25 meters

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Q. A person is standing 10 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. 5√3 meters
B. 10 meters
C. 15 meters
D. 20 meters

Solution

Height = distance * tan(60) = 10 * √3 = 10√3 meters.

Correct Answer: A — 5√3 meters

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Q. A person is standing 15 meters 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. 15√3 meters
B. 10 meters
C. 5 meters
D. 20 meters

Solution

Height = distance * tan(angle) = 15 * (1/√3) = 15/√3 = 15√3 meters.

Correct Answer: A — 15√3 meters

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Q. A person is standing 15 meters away from a tree. If the angle of elevation to the top of the tree is 45 degrees, what is the height of the tree?

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

Solution

Height = distance * tan(angle) = 15 * 1 = 15 meters.

Correct Answer: B — 15 meters

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Q. A person is standing 15 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. 15√3 meters
B. 10√3 meters
C. 20 meters
D. 25 meters

Solution

Height = distance * tan(60) = 15 * √3 = 15√3 meters

Correct Answer: A — 15√3 meters

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Q. A person is standing 25 meters 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. 25√3 meters
B. 30 meters
C. 35 meters
D. 40 meters

Solution

Height = distance * tan(60) = 25 * √3 = 25√3 meters.

Correct Answer: A — 25√3 meters

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Q. A person is standing 25 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. 15 meters
B. 20 meters
C. 25 meters
D. 30 meters

Solution

Height = distance * tan(37) = 25 * 0.7536 ≈ 18.84 meters, rounded to 20 meters.

Correct Answer: B — 20 meters

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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 30 degrees, what is the height of the pole?

A. 12.5 meters
B. 25 meters
C. 15√3 meters
D. 20 meters

Solution

Height = distance * tan(angle) = 25 * (1/√3) = 25/√3 ≈ 12.5 meters.

Correct Answer: A — 12.5 meters

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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 53 degrees, what is the height of the pole?

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

Solution

Height = distance * tan(angle) = 25 * tan(53°) ≈ 25 * 1.327 = 20.68 meters.

Correct Answer: B — 20 meters

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Q. A person is standing 25 meters away from a wall. If the angle of elevation to the top of the wall is 75 degrees, what is the height of the wall?

A. 24.5 meters
B. 25 meters
C. 26.5 meters
D. 27.5 meters

Solution

Height = distance * tan(75) = 25 * 3.732 = 93.3 meters.

Correct Answer: D — 27.5 meters

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Q. A person is standing 30 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. 30 meters
B. 45 meters
C. 60 meters
D. 75 meters

Solution

Height = distance * tan(45) = 30 * 1 = 30 meters.

Correct Answer: A — 30 meters

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Q. A person is standing 30 meters away 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. 30√3
B. 20√3
C. 10√3
D. 40√3

Solution

height = distance * tan(60) = 30 * √3 = 30√3 meters

Correct Answer: A — 30√3

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Q. A person is standing 30 meters away 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. 15√3 meters
B. 30 meters
C. 20√3 meters
D. 25 meters

Solution

Height = distance * tan(60) = 30 * √3 = 15√3 meters.

Correct Answer: A — 15√3 meters

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Q. A person is standing 40 meters 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 meters
B. 23 meters
C. 30 meters
D. 35 meters

Solution

Height = distance * tan(angle) = 40 * (1/√3) = 40 / 1.732 = 23.09 meters.

Correct Answer: A — 20 meters

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Q. A person is standing 40 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. 20 meters
B. 30 meters
C. 40 meters
D. 45 meters

Solution

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

Correct Answer: C — 40 meters

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Q. A person is standing 40 meters away from a tower. If the angle of elevation to the top of the tower is 45 degrees, what is the height of the tower?

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

Solution

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

Correct Answer: C — 40 meters

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Q. A person is standing 45 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. 30 meters
B. 45 meters
C. 60 meters
D. 75 meters

Solution

Height = distance * tan(angle) = 45 * 1 = 45 meters.

Correct Answer: B — 45 meters

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Q. A person is standing 50 meters 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 meters
B. 50 meters
C. 75 meters
D. 100 meters

Solution

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

Correct Answer: A — 25 meters

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Height and Distance

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