Question

problem 9: spiral review
a 12 - foot flagpole casts a shadow that is 5 feet long.
at the same time, a nearby telephone pole casts a shadow that
is 12.5 feet long.
what is the height of the telephone pole, x?
5.2 feet 15 feet
18.5 feet 30 feet

Explanation:

Step1: Set up proportion

Since the triangles are similar (same - time, so same - angle of elevation), the ratio of height to shadow length is equal. Let the height of the telephone pole be \(x\). We have the proportion \(\frac{\text{height of flagpole}}{\text{shadow of flagpole}}=\frac{\text{height of telephone pole}}{\text{shadow of telephone pole}}\), i.e., \(\frac{12}{5}=\frac{x}{12.5}\).

Step2: Cross - multiply

Cross - multiplying gives \(5x = 12\times12.5\).

Step3: Solve for \(x\)

First, calculate \(12\times12.5=150\). Then, \(x=\frac{150}{5}\).

Answer:

\(x = 30\) feet