Question

Wires are attached to a pole to make it more secure. The diagram shows one of those wires having a length of 220 feet. The angle of elevation from the ground to the top of the pole is 36. What is the height of the pole?

159.8 ft

374.3 ft

178.0 ft

129.3 ft

Answer 1

The wire, the pole and the segment joining the leg of the pole to the wire in the ground form a right triangle whose hypotenuse is the wire, and the side opposite to the angle 36° is the pole.

By right triangle trigonometry, sin36°=(opposite side)/(hypotenuse.)

Substituting, we have 0.588=(opposite side)/220, thus the length of the opposite side, which represents the length of the pole, is

0.588*220 ft=129.3 ft