Question

A tourist Looks out from the observation deck of the empire state building. The deck is a height of 931.1 ft. She sees her friend on the ground below At an angle of depression of 36°. How far is her friend from the empire state building?

Answer 1

Answer:

1281.55 ft

Explanation:

• The height of the tourist above the ground = 931.1 ft.

,

• The angle of depression of her friend from the tourist = 36°

The diagram below is an illustration of the problem:

The distance of her friend from the empire state building is labeled x above.

Using trigonometric ratios:

$\tan36\degree=\frac{931.1}{x}$

Cross multiply to begin solving for x:

$x\tan36\degree=931.1$

Divide both sides by tan 36

$\begin{gathered} \frac{x\tan36\degree}{tan\text{ }36}=\frac{931.1}{\tan36} \\ x=1281.55\text{ ft} \end{gathered}$

Her friend is approximately 1281.55 ft from the empire state building.