Question

1. a tree casts a shadow that is 24 ft long. a 4-ft tall young boy casts a shadow that is 3 ft long. the two triangles created are similar. how tall is the tree? (hint: draw a picture first!)

Explanation:

Step1: Define variables and set up proportion

Let \( h \) be the height of the tree. Since the triangles are similar, the ratios of corresponding sides are equal. So, \(\frac{\text{Height of tree}}{\text{Length of tree's shadow}}=\frac{\text{Height of boy}}{\text{Length of boy's shadow}}\), which gives \(\frac{h}{24}=\frac{4}{3}\).

Step2: Solve for \( h \)

Cross - multiply: \( 3h = 4\times24 \). Calculate \( 4\times24 = 96 \), so \( 3h=96 \). Then divide both sides by 3: \( h=\frac{96}{3}=32 \).

Answer:

The tree is 32 feet tall.