Question

A person is standing 50 ft from a statue. The person looks up at an angle of elevation of 8 degrees when staring at the top of the statue. Then the person looks down at an angle of 14 degrees when staring at the base of the statue. How tall is the statute to the nearest tenth of a foot?

Answer 1

Explanation:

The triangle ABC formed is shown in the attached photo. The height of the statue is BC = x + y

To determine the length of x, we will apply trigonometric ratio.

Tan # = opposite side/ adjacent side

Where

# = 8 degrees

Opposite side = x ft

Adjacent side = 50 feet

tan 8 = x/50

x = 50tan8

x = 50×0.1405 = 7.025 feet

To determine the length of y, we will apply trigonometric ratio.

Tan # = opposite side/ adjacent side

Where

# = 14 degrees

Opposite side = y ft

Adjacent side = 50 feet

tan 14 = y/50

x = 50tan14

x = 50×0.2493 = 12.465

Height of statue = 12.465 + 7.025 = 19.5 feet