From the top of a vertical tower, 310 feet above the the surface of the earth, the angle of depression to a doghouse is 24° 34'. How far is it from the doghouse to the foot of the tower? Round your
Answer to the nearest hundredth.
A)678.14ft
B)780.74 ft
C)662.55 ft
D)690.54 ft

Question

Quizplus · Accepted Answer

The correct answer is A because the angle of depression is the angle between the horizontal and the line of sight to the doghouse. The tangent of this angle is the ratio of the height of the tower to the distance from the doghouse to the foot of the tower. So, tan(24° 34') = 310/x, where x is the distance from the doghouse to the foot of the tower. Solving for x, we get x = 310/tan(24° 34') = 678.14 ft.

From the Top of a Vertical Tower, 310 Feet Above