Question

to find the height of a very tall pine tree, you place a mirror on 8 feet 144 feet 72 feet 36 feet

Explanation:

Step1: Set up proportion

Since the triangles are similar, \(\frac{\text{height of person}}{\text{distance from person to mirror}}=\frac{\text{height of tree}}{\text{distance from tree to mirror}}\). Let \(h\) be the height of the tree. So \(\frac{6}{2}=\frac{h}{24}\).

Step2: Solve the proportion

Cross - multiply: \(2h = 6\times24\). Then \(2h=144\). Divide both sides by 2: \(h=\frac{144}{2}\).

Answer:

72 feet