Question

1. a flagpole casts a shadow that is 12 ft long. a 6 - ft tall man casts a shadow that is 8 ft long. the two triangles created are similar. how tall is the flagpole? (hint: draw a picture first!)

Explanation:

Step1: Set up proportion

Since the two triangles are similar, the ratios of their corresponding sides are equal. Let $h$ be the height of the flag - pole. The ratio of the height to the shadow length of the man is the same as the ratio of the height to the shadow length of the flag - pole. So we have the proportion $\frac{h}{12}=\frac{6}{8}$.

Step2: Solve the proportion for $h$

Cross - multiply: $8h = 6\times12$. Then $8h=72$. Divide both sides by 8: $h=\frac{72}{8}=9$.

Answer:

9 ft