In the figure below, a person standing at point A notices that the angle of elevation to the top of the antenna is . A second person standing 37.0 feet farther from the antenna than the person at A finds the angle of elevation to the top of the antenna to be . How far is the person at A from the base of the antenna? Round your answer to the nearest feet.

Question

In the figure below, a person standing at point A notices that the angle of elevation to the top of the antenna is   . A second person standing 37.0 feet farther from the antenna than the person at A finds the angle of elevation to the top of the antenna to be   . How far is the person at A from the base of the antenna? Round your answer to the nearest feet.     ​

Quizplus · Accepted Answer

Let x be the distance between the person at A and the base of the antenna. Then, we can set up the following equations:

tan(11.5 degrees) = height of antenna/x
tan(13 degrees) = height of antenna/(x+37)

Solving for the height of the antenna using both equations and setting them equal to each other, we get:

height of antenna/x = height of antenna/(x+37)
x = 37/tan(13 degrees) 
x ≈ 191 ft

Therefore, the person at A is approximately 191 feet away from the base of the antenna. The best choice is C.

In the Figure Below, a Person Standing at Point a Notices