Question
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.
Ask by Fowler Pearson. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The windmill's shadow is 32 yards long.
Solution
To determine the length of the windmill's shadow, we can use the concept of similar triangles.
Given:
- **Crane**: 30 yards tall with a shadow of 16 yards.
- **Windmill**: 60 yards tall with an unknown shadow length.
Since both the crane and the windmill are casting shadows under the same lighting conditions, the ratios of their heights to their shadow lengths will be equal.
Set up the proportion:
\[
\frac{\text{Height of Crane}}{\text{Shadow of Crane}} = \frac{\text{Height of Windmill}}{\text{Shadow of Windmill}}
\]
\[
\frac{30}{16} = \frac{60}{x}
\]
Solve for \( x \):
\[
30x = 60 \times 16
\]
\[
30x = 960
\]
\[
x = \frac{960}{30}
\]
\[
x = 32
\]
**Answer:**
32
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
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.
