Plane Trigonometry

Question

A vertical cable television is standing on the side of the hill, which makes an angle of 25.0 degrees with the horizontal. Guy wires are attached 160 ft up the tower. What lengths of guy wires are needed to reach points 50.0 ft uphill and 80.0 ft downhill from the base of the tower?

Answer 1

I drew the setting. As for the down hill cable; side "a" is 80'ground. The height is side "b"=160. Side "c" is the cable.

Formula for "c".

a^2+b^2-2ab*cosγ=c^2

(80^2+160^2-2*80*160*cos115°)^.5=206.93ft.

This time we need side "b"uphill.

a^2+c^2-2ac*cosβ=b^2

(50^2+160^2-2*50*160*cos65°)^.5=146.076ft