Question

find the height of a flagpole as shown in the figure below, if it casts a shadow of 12 ft at the same time that the shadow of a 6 - ft person is 8 ft. ft

Explanation:

Step1: Set up proportion

Since the triangles are similar, \(\frac{\text{height of flagpole}}{\text{length of flagpole's shadow}}=\frac{\text{height of person}}{\text{length of person's shadow}}\). Let \(h\) be the height of the flagpole. So \(\frac{h}{12}=\frac{6}{8}\).

Step2: Solve for \(h\)

Cross - multiply: \(8h = 6\times12\). Then \(8h=72\). Divide both sides by \(8\): \(h=\frac{72}{8}=9\).

Answer:

\(9\)