trig homework help

Question

A communication tower (the side CB) is located at the top (the point C) of a steep hill. The angle of inclination of the hill is 58 degrees. A guy wire is to be attached to the top (the point B) of the tower and to the ground (the point A), 101 m downhill from the base of the tower (the side AC). The angle ∠BAC is 12 degrees.

Find the length of cable (the side AB) required for the guy wire. Your answer is 

Answer 1

Make a point D:

∠BAD = ∠BAC + ∠CAD = 12 + 58 = 70°

Using ΔCAD (a right triangle), and cos(θ) = adjacent/hypotenuse:

cos(58°) = AD/101

Segment AD = 101cos(58°) = 53.52 m

Now using ΔBAD (another right triangle), and cos(θ) = adjacent/hypotenuse:

cos(70°) = 53.52/x

x = 53.52/cos(70°) = 156.5 m