Question

A straight road slopes upward 14 degrees from the horizontal. A vertical telephone pole beside the road casts a shadow of 60 feet down the road. if the angle of elevation of the sun is 55 degrees, what is the height of the telephone pole?

Answer 1

draw a diagram.
Label these points:

T = top of pole
B = base of pole on road
S = tip of shadow on road
Draw a horizontal line from S to where it intersects the extension of TB below the road. Call that point C.

Now, we want the height h = BT
Let
x = SC
y = CB

Now, we have

y/60 = sin 14°
x/60 = cos 14°
(h+y)/x = tan 55°
Combine all that to get

(h+60sin14°)cot55° = 60cos14°
I get h = 68.63 feet