Question

The top of a tree makes angles s and t with Points K and L on the ground, respectively, such that the angles are complementary. Point K is x meters and Point L is y meters from the base of the tree.



In terms of x and y, find the height of the tree. Include your work.

Answer 1

use tangent ratio:
\[\tan (s) = \frac{x}{h}\]
\[\tan(s) = \frac{h}{y}\]
set equal and solve for h
\[\frac{x}{h} = \frac{h}{y} \rightarrow h^2 = xy\]
\[h = \sqrt{xy}\]