Question

From the top of a fire tower, a forest ranger sees his partner on the ground at an angle of depression of 40 degrees. If the tower is 45 feet in height, how far is the partner from the base of the tower, to the nearest tenth of a foot ?

Answer 1

Explanation:

Find the diagram to the question attached for proper elucidation

Using SOH CAH TOA

From the diagram AB is the height of the tower and it serves as the opposite side.

Distance of the partner from the base of the tower is the adjacent AC

Using TOA;

Tan40 = AB/AC

Tan40 = 45/AC

AC = 45/tan40

AC = 45/0.8391

AC = 53.63m

Hence the partner is 53.63m from the base of the tower