Question

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

Answer 1

Answer:

The height of the statue is 21.4 feet

Step-by-step 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

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

$y=50tan(16)$

$y=14.33727ft$

now, we can find x

In triangle DEF:

we can use trig formula

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

$x=50tan(8)$

$x=7.0270ft$

we can see that

height of statue =x+y

so, the height of statue is

$=14.33727+7.0270$

$=21.4ft$

Answer 2

The height of the statue to the nearest tenth of a foot is 21.4 ft and this can be determined by using the trigonometric properties

Given :

• A person is standing 50 ft from a statue.
• The person looks up at an angle of elevation $16^\circ$ when staring at the top of the statue.
• The person looks down at an angle of depression $8^\circ$ when staring at the base of the statue.

Refer to the diagram attached below.

From the diagram in triangle ABF:

$\rm tan(16)=\dfrac{a}{50}$

a = 14.33 ft

From the diagram in triangle DEF:

$\rm tan(8)=\dfrac{b}{50}$

b = 7.02 ft

Now, the height of the statue is given by:

$\rm Height = a +b$

Height = 14.33 + 7.02

Height = 21.4 ft

The height of the statue to the nearest tenth of a foot is 21.4 ft.

For more information, refer to the link given below:

https://brainly.com/question/17081568