Question

Angel is trying to find the height of a radio antenna on the roof of a local building. He stands at a horizontal distance of 18 meters from the building. The angle of elevation from his eyes to the roof (point A) is 21°, and the angle of elevation from his eyes to the top of the antenna (point B) is 39°. If his eyes are 1.72 meters from the ground, find the height of the antenna (the distance from point A to point B). Round your answer to the nearest meter if necessary.

Answer 1

If Angel is trying to find the height of a radio antenna on the roof of a local building. The height of the antenna (the distance from point A to point B) is 8m.

How to find the height?

Given data:

Horizontal distance = 18 meters

Angle of elevation from his eyes to the roof (point A) = 21°

Angle of elevation from his eyes to the top of the antenna (point B) = 39°

So,

AB= 18 × (Tan 39° - Tan 21°)

AB = 18 × ( 0.8098 - 0.3839)

AB = 18 × 0.4259

AB = 7.67

AB = 8m (Approximately)

Therefore the height of the antenna (the distance from point A to point B) is 8m.