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? 10.4 m 7.5 m 17.5 m 9.6 m

Explanation:

Step1: Set up proportion

Since the triangles are similar (by AA similarity, as the angles of elevation of the sun are equal), we can set up the proportion \(\frac{\text{height of man}}{\text{length of man's shadow}}=\frac{\text{height of building}}{\text{length of building's shadow}}\). Let \(h\) be the height of the building. So, \(\frac{2.1}{3.2}=\frac{h}{11.5}\).

Step2: Solve for \(h\)

Cross - multiply: \(3.2h = 2.1\times11.5\). First, calculate \(2.1\times11.5=24.15\). Then, \(h=\frac{24.15}{3.2}\).

Step3: Calculate the value of \(h\)

\(h=\frac{24.15}{3.2}=7.546875\approx7.5\) (rounded to one decimal place).

Answer:

7.5 m