Question

Lucy is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 21 meters from the building. The angle of elevation from her eyes to the roof (point A) is 21 and the angle of elevation from her eyes to the top of the antenna (point B) is 3 6 36 If her eyes are 1.58 meters from the ground, what is the height of the antenna (the distance from point A to point B)? Round your answer to the nearest meter if necessary.

a) 17 meters
b) 19 meters
c) 23 meters

Answer 1

Using trigonometry, we can determine that the height of the antenna is 14 meters.

Step-by-step explanation:

To find the height of the antenna (the distance from point A to point B), we can use trigonometry and the given information.

Let's define the height of the antenna as 'x'. By drawing a triangle, we can see that tan(36°) = x / 21. Solving for x gives us x = 21 * tan(36°).

Substituting the angle in degrees to radians gives us x = 21 * tan(36 * π/180). Evaluating this expression gives us x = 14 meters. Therefore, the height of the antenna is 14 meters.