Question

ava stands in front of a tower so the tip of her shadow meets the tip of the towers shadofeet long. the diagram is not drawn to scale.what is the height of the tower?feet

Explanation:

Step1: Set up the proportion

Since the triangles are similar (by AA similarity, as the sun's rays create equal angles), we can set up the proportion \(\frac{\text{height of Ava}}{\text{length of Ava's shadow}}=\frac{\text{height of tower}}{\text{length of tower's shadow}}\). Let \(h\) be the height of the tower. Ava's height is \(5\) ft, her shadow is \(4\) ft, and the tower's shadow is \(74.4\) ft. So the proportion is \(\frac{5}{4}=\frac{h}{74.4}\).

Step2: Solve for \(h\)

Cross - multiply: \(4h = 5\times74.4\). Then \(4h=372\). Divide both sides by \(4\): \(h=\frac{372}{4}\).

Answer:

\(93\)