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 degrees. To the nearest foot, what's the height of the pole?
To find the height of the pole, we can set up a right triangle with the pole forming the opposite side, the distance from the base to the surveyor forming the adjacent side, and the height of the transit forming the opposite side.
Using trigonometry, we can use the tangent function to solve for the height of the pole:
tan(36°) = height of pole / 120 feet
height of pole = tan(36°) * 120 feet
height of pole = 0.726542528 * 120 feet
height of pole ≈ 87.18 feet
Therefore, to the nearest foot, the height of the pole is 87 feet.