Question

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

Answer 1

`h=50.25\ ft`

Explanation:

Right Triangles

In a right triangle, one of the internal angles is 90°. When this happens, there is always a longer side, called hypotenuse and two shorter sides, called legs. They relate to Pythagoras's theorem. The basic trigonometric relations also stand, including

`\displaystyle tan\alpha=(a)/(c)`

where a is the opposite leg to
`\alpha` and c is its adjacent led .

In our problem, we have a statue being looked by a person in such a way that the top of the statue forms an angle of 8° with the horizontal and the base of the statue forms an angle of 14° down. We also know the distance from the person to the statue is 50 ft. The situation is shown in the image below.

The height of the statue is h=a+b, where

`a=50tan8^o`

`b=50tan14^o`

Thus

`h=50tan8^o+50tan14^o`

`h=50(tan8^o+tan14^o)`

`\boxed{h=50.25\ ft}`