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Shadow Problem – Tree Height
publish date: 2026/05/14 21:51:48.265419 UTC
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A person who is 6 feet tall casts a shadow 4 feet long. At the same time, a nearby tree casts a shadow 20 feet long. The triangles formed are similar. Find the height \(h\) of the tree.
Correct Answer
30 ft
Explanation
Since sun rays are parallel, the two right triangles are similar. Set up the proportion:
\[\frac{\text{person's height}}{\text{person's shadow}} = \frac{\text{tree's height}}{\text{tree's shadow}}\]
\[\frac{6}{4} = \frac{h}{20}\]
Cross multiply: \(4h = 6 \times 20 = 120\) → \(h = 30\). The tree is 30 feet tall.
Reference
go-math-science.com