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Building Height from a Stake's Shadow
publish date: 2026/05/14 21:51:48.553661 UTC
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A 3-foot stake held vertically in the ground casts a shadow 2 feet long. At the same time, a building casts a shadow 30 feet long. The triangles are similar. What is the height \(h\) of the building?
Correct Answer
45 ft
Explanation
The two similar triangles give the proportion:
\[\frac{3}{2} = \frac{h}{30}\]
Cross multiply: \(2h = 3 \times 30 = 90\) → \(h = 45\). The building is 45 feet tall.
Reference
go-math-science.com