Question

use similar triangles to solve. a person who is 6 feet tall is standing 182 feet from the base of a tree, and the tree casts a 196 foot shadow. the persons shadow is 14 feet in length. what is the height of the tree?

Explanation:

Step1: Set up proportion

Let \( h \) be the height of the tree. Since the triangles are similar, \(\frac{\text{height of person}}{\text{length of person's shadow}}=\frac{\text{height of tree}}{\text{length of tree's shadow}}\). The distance of the person from the tree (\(182\) ft) is extra information. The proportion is \(\frac{6}{14}=\frac{h}{196}\).

Step2: Cross - multiply

Cross - multiply the proportion: \(14h = 6\times196\).

Step3: Solve for \(h\)

First, calculate \(6\times196 = 1176\). Then, \(h=\frac{1176}{14}\). \(1176\div14 = 84\).

Answer:

\(84\)