Question

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

Answer 1

Answer:

The statue is 22.24 ft tall.

Step-by-step explanation:

The given question says that, the man is standing 50 ft away from the statue.

Looking at the top of the statue, the  angle of elevation is 8°.

Hence, where the man is standing, from that horizontal plane, the distance of the top of the statue is $50 tan 8°$.

Similarly, looking down towards the base, the angle is 14°.

Hence, the height from the base of the statue to the horizontal plane, where the man is standing is $50 tan 14°$.

The total height of the statue is $50 tan 8° + 50 tan 14° = 50( tan 8° + tan 14°)$ = 22.24475804 ≅22.24 ft.