Question

A man is standing 20 feet away from the base of a tree and looking at the top of a tree wondering it’s height. If the man’s eyes are located 6 feet off the ground and the angle of elevation is 67°, how tall is the tree? Round to the nearest tenth of a foot.

A) 53.1 feet
B) 18.1 feet
C) 47.1 feet
D) 39.0 feet

Answer 1

Answer:

The answer to your question is the letter A) 53.1 feet

Step-by-step explanation:

Data

Adjacent side = 20 ft

angle = Ф = 67°

distance from the eyes to the ground = 6 ft

Opposite side = ?

To solve this problem use trigonometric functions. The trigonometric function that relates the Opposite side and the Adjacent side is tangent.

tan Ф = Opposite side / Adjacent side

-Solve for Opposite side

Opposite side = Adjacent side x tan Ф

- Substitution

Opposite side = 20 x tan 67

-Simplification

Opposite side = 20 x 2.36

- Result

Opposite side = 47.1 ft

Height = 47.1 + 6

           = 53.1 ft