From the foot of a building I have to look upwards at an angle of 22degrees 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 50degrees to look at the top of the tree.

Question

From the foot of a building I have to look upwards at an angle of 22degrees 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 50degrees to look at the top of the tree.
a.  How tall is the tree?
How far from the building is the tree?

MathMate · Answer

Assume the observations were made from the same building. Let the distance of the building from the tree is D in m. Then D(tan22+tan50)=150 D=(150)/(tan22+tan50)

Bryan · Answer

93.99