Question

a 13.5 - foot ladder casts a shadow that is 36 feet long. a man who is 5.4 feet tall is standing next to the ladder. how long is the mans shadow? round your answer to the nearest hundredths. feet

Explanation:

Step1: Set up proportion

Let \(x\) be the length of the man's shadow. Since the ratio of height to shadow length is the same for both the ladder and the man, we have \(\frac{13.5}{36}=\frac{5.4}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(13.5x = 5.4\times36\).

Step3: Solve for \(x\)

First, calculate \(5.4\times36 = 194.4\). Then \(x=\frac{194.4}{13.5}\).
\(x = 14.4\)

Answer:

\(14.40\) feet