Question

frank wants to measure the height of a tree. he sights the top of the tree, using a mirror that is lying flat on the ground. the mirror is 37 ft from the tree, and frank is standing 8.1 ft from the mirror, as shown in the figure. his eyes are 5 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: Utilize the property of similar triangles

Since the two triangles (formed by Frank, the mirror and the tree) are similar. Let the height of the tree be \(h\). The ratio of corresponding sides of similar triangles is equal. We have the proportion \(\frac{h}{37}=\frac{5}{8.1}\).

Step2: Solve the proportion for \(h\)

Cross - multiply the proportion: \(h=\frac{5\times37}{8.1}\).
Calculate \(5\times37 = 185\), then \(h=\frac{185}{8.1}\approx22.84\).

Answer:

\(23\)