Question

A forest ranger spots a fire from a 21-foot tower. The angle of depression from the tower to the fire is 12 degrees . To the nearest foot, how far is the fire from the base of the tower?

Answer 1

Explanation:

98.8

Answer 2

99

Explanation:

The angle of depression looking from the tower is the same as the angle of elevation looking at the top of the tower from the spot of the fire. So, tan (12 degrees) = 21 / distance between the tower and fire. Thus, the distance = 21 / tan(12).

tan (12) = 0.2126

Distance = 21 / 0.2126 = 98.78

The question asks about the distance from the base to the fire (to the nearest foot.) Thus, it is 99 feet.