Question

A guy wire to the top of a tower makes an angle of 75 o with the level ground. At a point 40 feet farther from the base of the tower and in line with the base of the wire, the angle of elevation to the top of the tower is 20 o. What is the length of the guy wire?

Answer 1

Explanation:

See the picture in attached sheet. It shows the height of tower as h, length of wire as l.

Two right angled triangles are formed

From the triangles we make out that h/x=sin 75=0.9659

Or h =0.9659l

Base distance = l cos 75 = 0.2588l

From big right triangle, we have

tan 20 =

Or h =(0.2588l+40) (0.3640)

Equating two heights

0.9659l=(0.2588l+40) (0.3640)

=0.0942l+14.56

0.8717l=14.56

l=16.703 ft