Clara found that a crane that is 30 yards tall casts a shadow 16 yards long. Then Clara noticed a nearby windmill that is 60 yards tall. How long is the windmill's shadow? Write your answer as a whole number or a decimal. Do not round.
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To solve this, we can use the concept of similar triangles. Since the crane and its shadow form one triangle, and the windmill and its shadow form a second triangle, the ratios of their respective heights to the lengths of their shadows will be the same. The height of the crane is 30 yards, and it casts a shadow of 16 yards. The height of the windmill is 60 yards, and we can let the length of its shadow be \( x \) yards. We can set up the proportion: \[ \frac{30}{16} = \frac{60}{x} \] Cross-multiplying gives: \[ 30x = 60 \times 16 \] \[ 30x = 960 \] \[ x = \frac{960}{30} = 32 \] So, the windmill's shadow is 32 yards long.