From the foot of a building I have to look upwards at an angle of 22 degrees to sight the top of a tree. From the top of the building, 150m above ground level, I have to look down at an angle of 50 degrees below the horizontal to sigh the tree top.

Question

a.) How hight is the tree?
b.) How far from the building is this tree?

Answer 1

Let X be the distance from building t tree. H = tree height. Solve this set of equations:

H/X = tan 22
(150-H)/X = tan 50

(150-H)/H = tan 50/tan 22
This can be solved for H, using algebra and trig functions. Once you know H, solve for X.

Answer 2

h=94.3
x=37.7