Question

1. 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? 10.4 m 9.6 m 17.5 m 7.5 m

Explanation:

Step1: Set up proportion

Since the triangles are similar (by AA similarity, as the angle of elevation of the sun is the same for both the man and the building), the ratio of height to shadow length is equal. Let \(h\) be the height of the building. Then \(\frac{2.1}{3.2}=\frac{h}{11.5}\).

Step2: Solve for \(h\)

Cross - multiply: \(3.2h = 2.1\times11.5\). First, calculate \(2.1\times11.5=24.15\). Then \(h=\frac{24.15}{3.2}\approx7.5\) (rounded to one decimal place).

Answer:

\(7.5m\)