Asked by Shelley Nicole

From the foot of a building I have to look upwards at an angle of 22° to sight the top of a tree. From the top of a building, 150 meters above ground level, I have to look down at an angle of depression of 50° to look at the top of the tree.
a. How tall is the tree?
b. How far from the building is the tree?
Answered by Steve
assuming all these buildings are the same one, if the building is at distance d from the tree of height h,

draw a diagram to see that

(150-h)/d = tan 50°
h/d = tan 22°

plugging in the numbers,

h+1.19d = 150
h = 0.40d

So, we have

h = 94.3
d = 37.7