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, measure the angle of elevation to the top of the pole to be 36. To the nearest foot, what is the height of the pole?
First, let's draw a diagram to better understand the situation. The triangle formed by the surveyor, the pole, and the line of sight to the top of the pole is a right triangle. The angle of elevation is 36 degrees.
Let h be the height of the pole.
Using trigonometry, we can set up the following equation:
tan(36) = h / 120
tan(36) = h / 120
h = 120 * tan(36)
h ≈ 88.3 feet
Therefore, to the nearest foot, the height of the pole is approximately 88 feet.