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? (1 point) Responses
A. 87 feet
B. 95 feet
C. 71 feet
D. 79 feet
B. 95 feet
To find the height of the pole, we can use the tangent function.
tan(36°) = height of pole / 120 feet
height of pole = 120 feet * tan(36°)
height of pole ≈ 120 feet * 0.7265
height of pole ≈ 87.18 feet
Since the transit is 8 feet tall, we need to add the height of the transit to the height of the pole to get the total height of the pole:
Total height of pole = height of pole + height of transit
Total height of pole = 87.18 feet + 8 feet
Total height of pole = 95.18 feet
Rounded to the nearest foot, the height of the pole is 95 feet.