Question

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1. a boy who is 1.6 m tall casts a 2.4 m shadow when he stands 8.1 m from the base of an electric light pole. how high above the ground is the light globe?

Explanation:

Step1: Identify similar triangles

The two triangles (boy's triangle and light globe's triangle) are similar, so their corresponding sides are proportional. The boy's height is \(1.6\) m, his shadow length is \(2.4\) m. The light globe's shadow length is \(2.4 + 8.1=10.5\) m. Let the light globe's height be \(x\) m. So, \(\frac{1.6}{2.4}=\frac{x}{10.5}\).

Step2: Solve for \(x\)

Cross - multiply: \(2.4x = 1.6\times10.5\). Calculate \(1.6\times10.5 = 16.8\). Then, \(x=\frac{16.8}{2.4}\). Divide \(16.8\) by \(2.4\), we get \(x = 7\).

Answer:

The light globe is \(7\) meters above the ground.