Question

Frank stands 450 feet from the base of the Statue of Liberty. If the Statue of Liberty is 306 feet tall, what is the angle of depression from the top of the statue’s torch to Frank?

Round the answer to the nearest tenth.
A. 33.7°
B. 27.4°
C. 33.9°
D. 62.2°

Answer 1

A. 33.7

Explanation:

Make sure to Not use the full height of the Statue of Liberty (306 feet)

To find the answer you need to subtract 306 by 5.5 feet because you are measuring from Frank's line of sight not from his toes. You will get 300.5.

Answer 2

34.2 degrees.

Explanation:

Please find the attachment.

We have been given that Frank stands 450 feet from the base of the Statue of Liberty. If the Statue of Liberty is 306 feet tall. We are asked to find the angle of depression from the top of the statue’s torch to Frank.

Let x represent angle of depression.

We can see that angle of depression, Statue of liberty and Frank form a right triangle with respect to ground.

We know that tangent relates opposite side of right triangle with its adjacent side.

`\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}`

`\text{tan}(x)=(306)/(450)`

Now, we will inverse tangent to solve for x as:

`x=\text{tan}^(-1)((306)/(450))`

`x=34.215702132437^(\circ)`

`x\approx 34.2^(\circ)`

Therefore, the angle of depression would be approximately 34.2 degrees.