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)
Using trigonometry, we can set up a right triangle with the pole as the vertical side opposite the angle of 36°, the distance from the base of the pole as the adjacent side, and the height of the pole as the opposite side.
We can use the tangent function to find the height of the pole:
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
Therefore, to the nearest foot, the height of the pole is 87 feet.