QuestionMay 4, 2026

4. A person who is 5 feet tall casts a shadow that is 7 feet long. At the same time a nearby tree casts a shadow that is 21 feet long. How tall is the tree?

4. A person who is 5 feet tall casts a shadow that is 7 feet long. At the same time a nearby tree casts a shadow that is 21 feet long. How tall is the tree?
4. A person who is 5 feet tall casts a shadow that is 7 feet long. At the same time a
nearby tree casts a shadow that is 21 feet long. How tall is the tree?

Solution
4.3(278 votes)

Answer

15 feet Explanation 1. Set up similar triangles ratio Heights and shadow lengths are proportional: \frac{\text{Height}}{\text{Shadow length}} is constant. 2. Apply proportion \frac{5}{7} = \frac{h}{21} 3. Solve for h h = \frac{5}{7} \times 21 = 15

Explanation

1. Set up similar triangles ratio<br /> Heights and shadow lengths are proportional: $\frac{\text{Height}}{\text{Shadow length}}$ is constant.<br />2. Apply proportion<br /> $\frac{5}{7} = \frac{h}{21}$<br />3. Solve for $h$<br /> $h = \frac{5}{7} \times 21 = 15$
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