A survey team is trying to estimate the height of a mountain above a level plain.

Question

From one point on the plain, they observe that the angle of elevation to the top of the mountain is 32°

From a point 2000 feet closer to the mountain along the plain, they find that the angle of elevation is 35°

How high (in feet) is the mountain?

Answer 1

Draw and label a diagram!

A is the point of first observation

B is the point of second observation

C is the base of the mountain

D is the summit of the mountain

h represents the distance DC

x represents the distance BC

h / x = sin 35° → h = x sin 35°

h ./ (2000 + x) = sin 32° → h = (2000 + x) sin 32°

x sin 35° = (2000 + x) sin 32°

Solve for x. Then use the vale of x and tan 35° to determine h.