Question

use similar triangles to solve. a person who is 5 feet tall is standing 143 feet from the base of a tree, and the tree casts a 156 foot shadow. the persons shadow is 13 feet in length. what is the height of the tree?

Explanation:

Step1: Define Variables for Similar Triangles

Let \( h \) be the height of the tree. The person's height is 5 ft, person's shadow is 13 ft, tree's shadow is 156 ft. Since triangles are similar, ratios of height to shadow length are equal: \(\frac{h}{156}=\frac{5}{13}\).

Step2: Solve for \( h \)

Cross - multiply: \( 13h = 5\times156 \). Calculate \( 5\times156 = 780 \). Then \( h=\frac{780}{13}=60 \).

Answer:

The height of the tree is 60 feet.