Question

kala 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. kala is standing 8.7 ft from the mirror, as shown in the figure. her eyes are 5 ft above the ground. how tall is the tree? (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 $\frac{h}{33}=\frac{5}{8.7}$.

Step2: Solve for $h$

Cross - multiply: $8.7h = 33\times5$. Then $8.7h=165$. Divide both sides by $8.7$: $h=\frac{165}{8.7}\approx18.97$.

Answer:

$18.97$