Question

use similar triangles to solve. a person who is 5 feet tall is standing 144 feet from the base of a tree, and the tree casts a 156 - foot shadow. the persons shadow is 12 feet in length. what is the height of the tree?

Explanation:

Step1: Set up proportion

Since the triangles formed by the person, their shadow and the tree, its shadow are similar, the ratios of height to shadow - length are equal. Let $h$ be the height of the tree. The proportion is $\frac{\text{height of person}}{\text{length of person's shadow}}=\frac{\text{height of tree}}{\text{length of tree's shadow}}$, i.e., $\frac{5}{12}=\frac{h}{156}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{5}{12}=\frac{h}{156}$ gives $12h = 5\times156$.

Step3: Solve for $h$

First, calculate $5\times156 = 780$. Then, $h=\frac{780}{12}=65$.

Answer:

65