Question

A cellular telephone tower that is 180 feet tall is placed on top of a mountain that is 1200 feet above sea level. What is the angle of depression from the top of the tower to a cell phone user who is 6 horizontal miles away and 200 feet above sea level? (Round your answer to two decimal places.)

Answer 1

2.13°

Explanation:

The mnemonic SOH CAH TOA reminds you of the relation between the sides of a right triangle and the corresponding angle.

Here, the difference in elevation between the tower top and the user is ...

(1200 +180) -200 = 1180 . . . . feet

The horizontal distance from the tower to the user is ...

(6 mi)(5280 ft/mi) = 31,680 ft

Then the angle of elevation α satisfies ...

tan(α) = opposite/adjacent = (1180 ft)/(31,680 ft) ≈ 0.0372475

α = arctan(0.0372475) ≈ 2.13°

The angle of depression is about 2.13°.