Francis needs to know the height of a tree from a given point on the ground.The finds that the elevation to the top of the tree is 36.70 he then moves 50 feet from the second point the angle of elevation to the top of the tree is 22.2 find the height of the tree?

Calling the heighth of the tree x, the distance to the first measurement y, the first angle a=36.7, and the second angle b=22.2, we have cot a=y/x, so y=x cot a. Also cot b = (y+50)/x = (x cot a + 50)/x = cot a + 50/x, so 50/x = cot b - cot a and so x =
50/(cot b-cot a).

Calling the heigth of the tree x, the distance to the first measurement y, the first angle a=36.7, and the second angle b=22.2, we have cot a=y/x, so y=x cot a. Also cot b = (y+50)/x = (x cot a + 50)/x = cot a + 50/x, so 50/x = cot b - cot a and so x =
50/(cot b-cot a).