Question

a telephone pole 10 meters tall cast a shadow 8 meters long at the same time that a tree nearby casts a shadow 14 meters long. how tall is the tree? the height of the tree is blank meters. possible points: 1.92

Explanation:

Step1: Set up proportion

Let \( h \) be the height of the tree. Since the ratios of height to shadow length are equal (similar triangles), we have \(\frac{10}{8}=\frac{h}{14}\).

Step2: Solve for \( h \)

Cross - multiply: \(8h = 10\times14\). Then \(8h=140\). Divide both sides by 8: \(h=\frac{140}{8}=\frac{35}{2} = 17.5\).

Answer:

\(17.5\)