Question

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°. To the nearest foot, what is the height of the pole?

Answer 1

Taking the tangent of the 44° angle, knowing tan = opp/adj, we can do:
tan 44° = x/140
x = 140 tan 44°
x approx = 140 * 0.9657 = 135.198
Remembering to add in the 4 feet, we get that:
The pole is approx 135.198 + 4 feet tall, aka
139.198 ft
This makes intuitive sense because the angle