Height and Distance: Mastering Concepts for Competitive Exams

Height and Distance

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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