Question

a person is standing 50 ft from a statue. The person looks up at an angle of elevation of 16 degrees when staring at the top. Then the person looks down at an angle of depression of 8 degrees when staring at the base of the statue. How tall is the statue to the nearest tenth of a foot?

Answer 1

The height of the statue is 21.4 feet

Explanation:

We are given

A person is standing 50 ft from a statue

The person looks up at an angle of elevation of 16 degree when staring at the top of the statue

hen the person looks down at an angle of depression of 8 degree when staring at the base of the statue

Firstly, we will draw diagram

In triangle ABF:

FC=50

we can use trig formula

tan(16)=\frac{y}{50}tan(16)=50y

y=50tan(16)y=50tan(16)

y=14.33727fty=14.33727ft

now, we can find x

In triangle DEF:

we can use trig formula

tan(8)=\frac{x}{50}tan(8)=50x

x=50tan(8)x=50tan(8)

x=7.0270ftx=7.0270ft

we can see that

height of statue =x+y

so, the height of statue is

=14.33727+7.0270=14.33727+7.0270

=21.4ft=21.4ft