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 79 feet 79 feet 71 feet 71 feet 87 feet 87 feet 95 feet
To find the height of the pole, we can set up a right triangle with the pole as the vertical side, the distance from the pole as the base, and the transit as the opposite side to the angle of elevation.
Using trigonometry, we know that:
tan(angle) = opposite/adjacent
tan(36°) = height/120 feet
height = 120 feet * tan(36°)
height ≈ 87 feet
Therefore, the height of the pole is approximately 87 feet.