Question

a man who is 70 inches tall has a shadow that is 80 inches long. a nearby tree casts a shadow that is 164 inches long. the shadow of the man and the shadow of the tree form similar triangles. how tall is the tree in inches? (1 point)

Explanation:

Step1: Set up the proportion

Since the triangles are similar, the ratio of height to shadow length is the same. Let \(h\) be the height of the tree. Then \(\frac{\text{Man's height}}{\text{Man's shadow}}=\frac{\text{Tree's height}}{\text{Tree's shadow}}\), so \(\frac{70}{80}=\frac{h}{164}\).

Step2: Solve for \(h\)

Cross - multiply: \(80h = 70\times164\). First, calculate \(70\times164=11480\). Then \(h=\frac{11480}{80}\). Simplify \(\frac{11480}{80}=\frac{1148}{8}=143.5\).

Answer:

\(143.5\) inches