The angle of elevation from a point on the ground to the top of a tree is 39.8 degrees. The angle of elevation from a point 51.7 ft farther back to the top of the tree is 19.7 degrees. Help find the height of the tree.

Answer 1

well, you know that

h/x = tan 39.8°
h/(x+51.7) = tan 19.7°

Now eliminate x and solve for h:

h/tan39.8° = h/tan19.7° - 51.7
1.2h = 2.8h - 51.7
h = 32.3

check my math, but that's the method to my madness.