Height and Distance: Mastering Concepts for Competitive Exams

Height and Distance

Q. From the top of a hill, the angle of depression to a car parked on the road is 30 degrees. If the height of the hill is 60 meters, how far is the car from the base of the hill?

A. 60√3 meters
B. 30√3 meters
C. 90 meters
D. 120 meters

Solution

Distance = height / tan(angle) = 60 / (1/√3) = 60√3 meters.

Correct Answer: A — 60√3 meters

Q. From the top of a tower, the angle of depression to a point on the ground is 30 degrees. If the height of the tower is 50 meters, how far is the point from the base of the tower?

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

Solution

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

Correct Answer: A — 25√3 meters

Q. If a 12-meter tall pole casts a shadow of 8 meters, what is the angle of elevation of the sun?

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

Solution

tan(θ) = height / shadow = 12 / 8 = 1.5; θ = tan^(-1)(1.5) ≈ 56.31 degrees

Correct Answer: C — 53.13 degrees

Q. If a kite is flying at a height of 100 meters and the angle of elevation from a point on the ground is 60 degrees, how far is the point from the base of the kite?

A. 50 meters
B. 100 meters
C. 150 meters
D. 200 meters

Solution

Distance = height / tan(60) = 100 / √3 = 100/√3 = 50 meters

Correct Answer: A — 50 meters

Q. If a kite is flying at a height of 60 meters and 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's vertical line?

A. 30 meters
B. 20√3 meters
C. 60 meters
D. 40 meters

Solution

Distance = height / tan(angle) = 60 / (√3) = 20√3 meters.

Correct Answer: B — 20√3 meters

Q. If a person is 20 meters away from a tree and the angle of elevation to the top of the tree is 45 degrees, what is the height of the tree?

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

Solution

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

Correct Answer: B — 20 meters

Q. If a person is standing 15 meters away from a building and the angle of elevation to the top of the building is 30 degrees, what is the height of the building?

A. 7.5 meters
B. 10 meters
C. 12.5 meters
D. 15 meters

Solution

Height = distance * tan(30) = 15 * (1/√3) = 15/√3 = 5√3 meters ≈ 7.5 meters.

Correct Answer: A — 7.5 meters

Q. If a person standing 15 meters away from a building sees the top of the building at an angle of elevation of 30 degrees, what is the height of the building?

A. 7.5 meters
B. 10 meters
C. 12.5 meters
D. 15 meters

Solution

Height = distance * tan(30) = 15 * (1/√3) = 15/√3 = 5√3 meters ≈ 7.5 meters.

Correct Answer: A — 7.5 meters

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