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

Learn More →

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

Learn More →

Q. A person is 12 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. 6 meters
B. 12 meters
C. 18 meters
D. 24 meters

Solution

Height = distance * tan(30) = 12 * (1/√3) = 12/√3 = 4√3 meters ≈ 6 meters.

Correct Answer: A — 6 meters

Learn More →

Q. A person is 25 meters away from a cliff. If the angle of elevation to the top of the cliff is 45 degrees, what is the height of the cliff?

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

Solution

Height = distance * tan(45) = 25 * 1 = 25 meters.

Correct Answer: A — 25 meters

Learn More →

Q. A person is 25 meters away from a tower and sees the top of the tower at an angle of elevation of 30 degrees. What is the height of the tower?

A. 12.5 meters
B. 25 meters
C. 25√3 meters
D. 50 meters

Solution

Using tan(30) = height/distance, height = distance * tan(30) = 25 * (1/√3) = 25/√3 meters.

Correct Answer: A — 12.5 meters

Learn More →

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

Solution

Height = distance * tan(30) = 40 * (1/√3) = 40/√3 = 20√3 meters.

Correct Answer: A — 20√3 meters

Learn More →

Q. A person is 40 meters away from a tower. If the angle of elevation to the top of the tower is 30°, what is the height of the tower?

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

Solution

Using tan(30°) = height/40, height = 40 * tan(30°) = 40 * (1/√3) = 23.09 meters, approximately 20 meters.

Correct Answer: A — 20 meters

Learn More →

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

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

Solution

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

Correct Answer: A — 25√3 meters

Learn More →

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

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

Solution

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

Correct Answer: A — 25√3 meters

Learn More →

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

Learn More →

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

Learn More →

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

Learn More →

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

Learn More →

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

Learn More →

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

Learn More →

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

Learn More →

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

Learn More →

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

Learn More →

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

Learn More →

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

Learn More →

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

Learn More →

Q. A person is standing 30 meters away from a building. If the angle of elevation to the top of the building is 60°, what is the height of the building?

A. 15√3 meters
B. 30 meters
C. 15 meters
D. 20 meters

Solution

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

Correct Answer: A — 15√3 meters

Learn More →

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

Learn More →

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

Learn More →

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

Learn More →

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

Learn More →

Q. A person is standing 40 meters away from a statue. If the angle of elevation to the top of the statue is 60 degrees, what is the height of the statue?

A. 20√3 meters
B. 40√3 meters
C. 60√3 meters
D. 80√3 meters

Solution

Height = distance * tan(60) = 40 * √3 = 20√3 meters.

Correct Answer: A — 20√3 meters

Learn More →

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

Learn More →

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

Learn More →

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

Learn More →

Showing 61 to 90 of 163 (6 Pages)

Height and Distance

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?