Question

The angle of elevation of the mountain is 54o. The base of the mountain is 700 ft. What is the height of the mountain? Round your answer to a nearest foot. Show your work.

Answer 1

Given:

The angle of elevation of the mountain is 54 degrees.

The base of mountain is 700 ft.

The objective is to calculate the height of the mountain.

Using trigonometric ratio,

$\begin{gathered} \tan 54^{\circ}=\frac{perpendicular}{\text{base}} \\ =\frac{height}{700} \end{gathered}$

Solving for height,

$\begin{gathered} \text{height}=700\times\tan 54^{\circ} \\ =700\times1.37638192047 \\ =963.46734428\text{ ft} \end{gathered}$

Therefore, value of x = 963 ft.