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 40 degrees. to the nearest foot, what is the height of the pole?

Answer 1

using the law of sines, we can compute the height of the pole.

SinA / a = SinB / b = SinC / c (where the capital letter is the angle)

Since we know the pole is straight, we have a 90 degree angle for C and the angle of elevation to the top of the pole is 40 (A)...this means the remaining angle is 50 degrees (B)

Sin50 / 140 = Sin40 / a (multiply both sides by a)
aSin50 / 140 = Sin40 (multiply both sides by 140)
aSin50 = 140Sin40 (divide both sides by Sin50)
a = 140Sin40 / Sin50
a = 117.47 (round to the nearest foot)
a = 117 is the height of the pole