The angle of elevation of the top of a tower is 27 degrees from point A due east of it. The angle of elevation of the top of the tower is 11 degrees from another point B due south of the tower. Find the height of the tower if the distance AB is 40m.

Answer 1

If we label the top of the tower T and the bottom Q, then we have

tan 27° = PQ/QA
tan 11° = PQ/QB
QA^2 + QB^2 = 40

(PQ/tan27°)^2 + (PQ/tan11°)^2 = 40^2
Now just solve for PQ, the height of the tower.

Answer 2

Solving after steve's step:
(PQ/tan27°)^2 + (PQ/tan11°)^2 = 40^2
Take PQ^2 out as it is common to both:
PQ^2(1/tan27^2 + 1/tan11^2)= 1600
PQ^2=1600/(1/tan27^2 + 1/tan11^2)
PQ=√1600/(1/tan27^2 + 1/tan11^2)
PQ=7.26( 3 significant figures)