Question

a man whose height is 2.1 m casts a shadow that is 3.2 m in length. what is the approximate height of a building that casts a shadow of 11.5 m? 2.1 m 3.2 m 11.5 m 10.4 m 17.5 m 7.5 m 9.6 m

Explanation:

Step1: Set up proportion

Since the triangles are similar, \(\frac{\text{Man's height}}{\text{Man's shadow}}=\frac{\text{Building's height}}{\text{Building's shadow}}\). Let \(h\) be the building's height. So \(\frac{2.1}{3.2}=\frac{h}{11.5}\).

Step2: Solve for \(h\)

Cross - multiply: \(3.2h = 2.1\times11.5\). Then \(h=\frac{2.1\times11.5}{3.2}\). Calculate \(2.1\times11.5 = 24.15\). So \(h=\frac{24.15}{3.2}\approx7.5\).

Answer:

\(7.5\ m\)