Question

example 2: a tree casts a shadow that is 24 feet long. a person who is 5 feet tall is standing in front of the tree, and his shadow is 8 feet long. approximately how tall is the tree?

Explanation:

Step1: Set up proportion

Since the triangles are similar (due to same - angle sunlight), we can set up the proportion \(\frac{\text{height of tree}}{\text{length of tree's shadow}}=\frac{\text{height of person}}{\text{length of person's shadow}}\). Let \(h\) be the height of the tree. So, \(\frac{h}{24}=\frac{5}{8}\).

Step2: Solve for \(h\)

Cross - multiply: \(8h = 24\times5\). Then \(8h=120\). Divide both sides by 8: \(h=\frac{120}{8}=15\).

Answer:

15 feet