Question

diane wants to measure the height of a tree. she sights the top of the tree, using a mirror that is lying flat on the ground. the mirror is 34 ft from the tree, and diane is standing 5.6 ft from the mirror, as shown in the figure. her eyes are 6 ft above the ground. how tall is the tree? round your answer to the nearest foot. (the figure is not drawn to scale.)

Explanation:

Step1: Set up proportion

Since the angles of incidence and reflection are equal, the two right - angled triangles formed are similar. Let the height of the tree be $h$. The proportion is $\frac{h}{34}=\frac{6}{5.6}$.

Step2: Solve for $h$

Cross - multiply to get $h=\frac{6\times34}{5.6}$.
$h=\frac{204}{5.6}\approx36.43$.

Answer:

36 ft