Answer
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Step 1:: Write down the given information and the proportion for the problem.
\frac{\text{Bigger triangle height}}{\text{Bigger triangle base}} = \frac{\text{Smaller triangle height}}{\text{Smaller triangle base}}
The given information is: - The height of the tree (bigger triangle) is 32 feet. - The length of the tree's shadow (base of the bigger triangle) is 12 feet. - Jack's height (smaller triangle) is 6 feet. - We need to find the length of Jack's shadow (x, the base of the smaller triangle). The proportion is:
Step 2:: Plug the given values into the proportion and solve for the unknown.
x = \frac{6 \times 12}{32} = \frac{72}{32} = 2.25~\text{feet}
Cross-multiply to solve for x: Divide both sides by 32:
Final Answer
Jack's shadow is 2.25 feet long.
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