Question

sam needs to know the height of an electricity (power) pole in his neighborhood. the pole casts a 24 - foot shadow while he casts a 4 - foot shadow. sam is 6 feet tall. the height of the electricity pole is ____ feet tall. enter only the number.

Explanation:

Step1: Set up proportion

Since the triangles formed by Sam and his shadow, and the pole and its shadow are similar, we can set up the proportion \(\frac{\text{Sam's height}}{\text{Sam's shadow}}=\frac{\text{Pole's height}}{\text{Pole's shadow}}\). Let \(h\) be the height of the pole. We know Sam's height is \(6\) feet, Sam's shadow is \(4\) feet, and the pole's shadow is \(24\) feet. So the proportion is \(\frac{6}{4}=\frac{h}{24}\).

Step2: Solve for \(h\)

Cross - multiply: \(4h = 6\times24\). Then \(4h=144\). Divide both sides by \(4\): \(h=\frac{144}{4}\).

Answer:

\(36\)