Question

a boy, who is 5 ft. 6 in. tall, casts a shadow 2 ft long. find the height of the pole if it casts a shadow 2 yards long. 195 inches 198 inches 192 inches

Explanation:

Step1: Convert units

Since \(1\) foot \( = 12\) inches, the boy's height \(h_{1}=5\space ft\space6\space in=5\times12 + 6=66\) inches. The boy's shadow length \(s_{1}=2\space ft = 2\times12=24\) inches. The pole's shadow length \(s_{2}=2\) yards. Since \(1\) yard \( = 36\) inches, \(s_{2}=2\times36 = 72\) inches.

Step2: Set up proportion

Assume the height of the pole is \(h_{2}\). Using the proportion \(\frac{h_{1}}{s_{1}}=\frac{h_{2}}{s_{2}}\) (similar - triangles property). Substitute \(h_{1} = 66\), \(s_{1}=24\), and \(s_{2}=72\) into the proportion: \(\frac{66}{24}=\frac{h_{2}}{72}\).

Step3: Solve for \(h_{2}\)

Cross - multiply: \(24h_{2}=66\times72\). Then \(h_{2}=\frac{66\times72}{24}\). First, \(66\times72 = 4752\), and \(4752\div24=198\).

Answer:

198 inches