What is the height o the tree?

Question

Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is

H=60°, and from a second position L=20 feet farther along this path it is B=40°.  

What is the height of the​ tree?

Answer 1

Draw and label a diagram

T is the base of the tree

A is the first observation point

B is the second observation point

h is the height of the tree

AT / h = cot 60º

AT = h cot 60º

BT / h = cot 40º

BT = h cot 40º

AT + 20 = h cot 40º

AT = h cot 40º - 20

h cot 60º = h cot 40° - 20

Can you solve for h and answer?