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?

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