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.

Question

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?

Steve · Answer

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