the height of a tower....?

Question

a transmission tower is planted on a slope of a hill wic is elevated at an angle of 17'15' to the horizontal. the angle of depression of the top of the tower from a point Q, wic is situated at a distance of 150m from the foot of the tower up the hill, is 9'38'. Find the height of the tower.

thanks 4 your help :)

Answer 1

If you draw a diagram showing the tower, the hill, and the line joining Q with the top of the tower, you will have a triangle. One leg of the triangle is 150m. The angle opposite this side is a = 90º - 9º 38'. The angle between the tower and the hill is b = 90º - 17º 15'. The remaining angle in the triangle is c = 180º - a - b. Angle c is opposite the tower height. Using the law of sines:

150/sin(a) = h/sin(c).

Solve for h.