SOLUTION: A ranger's tower is located 44 meter from a tall tree. From the top of the tower, the angle of elevation to the top of the tree is 29 degrees, and the angle of depression to the ba

Algebra ->  Triangles -> SOLUTION: A ranger's tower is located 44 meter from a tall tree. From the top of the tower, the angle of elevation to the top of the tree is 29 degrees, and the angle of depression to the ba      Log On


   

Question 775771: A ranger's tower is located 44 meter from a tall tree. From the top of the tower, the angle of elevation to the top of the tree is 29 degrees, and the angle of depression to the base of the tree is 36 degrees. How tall is the tree?
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
You described two triangles, each which share a common side (leg of two right triangles) of 44 meters. The tangent of each of the angles is y%2F44, for two different values of y. You know each angle already. Use meaning of tangent as sine%28x%29%2Fcosine%28x%29=tangent%28x%29.

Here, you would have y%2F44=tan%28x%29.
You do not need to worry about the signs too much because you are really only interested in lengths.

These are the two lengths along the tree that you want:
y%5Bu%5D=44%2Atan%2829%29 and y%5Bd%5D=44%2Atan%2836%29, and then you want y%5Bu%5D%2By%5Bd%5D.