Question

You are skiing down a mountain with a vertical height of 700 feet. The distance from the top of the mountain to the base is 1400 feet. What is the angle of elevation from the base to the top of the mountain?

(Answer in degrees)

Answer 1

The angle of elevation from the base to the top of the mountain is 30°

Explanation:

The vertical height of the mountain h=700 feet

The distance of the top of the mountain from the base=1400 feet

The system is a right a triangle and we have to determine the angle of elevation from the base to the top of the mountain.

The hypotenuse of the triangle=1400 feet

Let α be the angle between the base of the mountain and the line joining the base to the top of the mountain

`sin\alpha =opposite side/hypotenuse\\=height h/hypotenuse\\=700/1400\\=0.5\\\\\alpha =sin^-1 (0.5)=30 \°`

The angle of elevation is 30°