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

Answer 1

Let x = length of flag pole from the transit
then
tan(60) = x/90

Answer 2

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