Solve the problem.
-A vertical antenna is mounted atop a 23-ft pole. From a point on the level ground 57 feet from the base of the pole, the antenna subtends an angle of 10.1°. Find the length of the antenna to the nearest tenth of a foot.
A) 32.4 ft
B) 8.8 ft
C) -12.8 ft
D) 12.7 ft

Question

Quizplus · Accepted Answer

The length of the antenna can be found using the tangent of the angle it subtends from the point on the ground. The tangent of an angle in a right triangle is the ratio of the opposite side (the length of the antenna plus the pole) to the adjacent side (the distance from the point to the base of the pole). Thus, $\tan(10.1°) = \frac{\text{antenna length} + 23}{57}$. Solving for the antenna length gives approximately 12.7 ft.

Solve the Problem. -A Vertical Antenna Is Mounted Atop a 23-Ft Pole. from 23-Ft