Question

Deepa is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 27 meters from the building. The angle of elevation from her eyes to the roof (point A) is 35 degrees, and the angle of elevation from her eyes to the top of the antenna (point B) is 41 degrees. If her eyes are 1.69 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.

a. 7 meters
b. 11 meters
c. 14 meters
d. 19 meters

Answer 1

The height of the antenna is approximately 19 meters.

Step-by-step explanation:

To find the height of the antenna, we can use the concept of trigonometry. We can form a right triangle with the horizontal distance of 27 meters as the base, the height of the antenna as the opposite side, and the line connecting Deepa's eyes to the roof of the building as the hypotenuse. Using the tangent function, we have:

tan(35 degrees) = height of antenna / 27 meters

height of antenna = 27 meters * tan(35 degrees) = 19 meters

Therefore, the height of the antenna is approximately 19 meters.