To find the height of a pole, a surveyor moves 120 feet away from the base of the pole and then, with a transit 8 feet tall, measures the angle of elevation to the top of the pole to be 36°. To the nearest foot, what is the height of the pole?

Question

(1 point)
Responses

87 feet
87 feet

95 feet
95 feet

71 feet
71 feet

79 feet

Answer 1

To solve this problem, we can use the tangent function:

tangent(angle) = opposite/adjacent

In this case, the angle of elevation is 36° and the opposite side is the height of the pole that we want to find, and the adjacent side is the distance between the surveyor and the base of the pole (120 feet + 8 feet for the height of the transit).

tan(36°) = height/128 feet

Using a calculator, we find:

height = tan(36°) * 128 feet
height ≈ 87.152 feet

To the nearest foot, the height of the pole is 87 feet.