To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to be 44°
44
°
. To the nearest foot, what is the height of the pole?
Let h be the height of the pole.
Using trigonometry, we can set up the following equation:
tan(44°) = h / 140
tan(44°) = h / 140
h = tan(44°) * 140
h ≈ 140 * 1.0665
h ≈ 149.31
Therefore, the height of the pole is approximately 149 feet.