Question

Two poles on the ground are 90 feet apart. The shorter pole is 7.5 feet tall. The angle of depression

from the top of the taller pole to the top of the shorter pole is 28°. How tall is the longer pole? Round
to the nearest tenth.

Answer 1

The longer pole is approximately 55.4 ft tall

Explanation:

Modeling the description will help you visualize and find the answer easier. By alternate interior angles theorem, the angle at the bottom (shown in picture below) is congruent to the angle of depression. Therefore, we can use tangent to find x.

tan 28=x/90

x=90*tan 28 (isolate the variable)

x is approx 47.9

to find the pole's height, you must add the shorter pole's height as well

h is approx 47.9+7.5

therefore, the longer pole's height is approx 55.4 ft tall