Question

A person standing at point C measures the angle of elevation to a point, A, at the top of a perpendicular cliff, to be 18°. After moving 2,200 feet directly toward the foot of the cliff, the person measures the angle of elevation to point A as 56°.

Answer 1

915

Explanation:

Answer 2

It would be helpful if the problem is drawn since we can easily picture out the situation. We would see that there are two right triangles one would have the angle 56 degrees which has a base equal to x ft and the other triangle has an angle of 18 degrees which has a base equal to 2200 + x ft. We can solve as follows:

let h as the height of the cliff,

tan 56 = h/x
tan 18 = h/(2200 + x)

solving simultaneously,
h = 915.46 ft
x = 617.48 ft

The height would be 915.46 ft.