Question

proving similar triangles practice
complete this assessment to review what youve learned. it will not count toward your grade.
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 ratios of corresponding sides are equal. Let \(h\) be the height of the tree. Then \(\frac{\text{height of man}}{\text{length of man's shadow}}=\frac{\text{height of tree}}{\text{length of tree's shadow}}\), so \(\frac{70}{80}=\frac{h}{164}\).

Step2: Solve the proportion 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:

\(143.5\)