Question

ava stands in front of a tower so the tip of her shadow meets the tip of the towers shadow. ava is 5 feet tall and casts a shadow tall and casts a shadow that is 74.4 feet long. the diagram is not drawn to scale. what is the height of the tower?

Explanation:

Step1: Set up proportion

Since the triangles are similar (by AA similarity, as the sun's angle is the same for both Ava and the tower), we can set up the proportion \(\frac{\text{Ava's height}}{\text{Ava's shadow length}}=\frac{\text{Tower's height}}{\text{Tower's shadow length}}\). Let \(h\) be the height of the tower. Ava's height is \(5\) feet, Ava's shadow length is \(4\) feet, and the tower's shadow length is \(74.4 + 4=78.4\) feet. So the proportion is \(\frac{5}{4}=\frac{h}{78.4}\).

Step2: Solve for \(h\)

Cross - multiply: \(4h=5\times78.4\). Then \(4h = 392\). Divide both sides by \(4\): \(h=\frac{392}{4}\).

Answer:

\(h = 98\) feet.