Question

use similar triangles to solve. a person who is 5 feet tall is standing 72 feet from the base of a tree, and the tree casts a 80 foot shadow. the persons shadow is 8 feet in length. what is the height of the tree? the height is

Explanation:

Step1: Set up the proportion

Since the triangles are similar, the ratio of height to shadow length is the same. Let \( h \) be the height of the tree. The proportion is \(\frac{\text{Person's height}}{\text{Person's shadow}}=\frac{\text{Tree's height}}{\text{Tree's shadow}}\), so \(\frac{5}{8}=\frac{h}{80}\).

Step2: Solve for \( h \)

Cross - multiply: \( 8h = 5\times80 \). Then \( 8h=400 \). Divide both sides by 8: \( h=\frac{400}{8} \).

Answer:

\( 50 \) ft