To find the length of the arc intercepted by a central angle in a circle, you can use the formula:
\[ L = \frac{\theta}{360} \times 2\pi r \]
where:
- \( L \) is the length of the arc,
- \( \theta \) is the central angle in degrees,
- \( r \) is the radius of the circle.
Plugging in the given values:
- \( \theta = 42 \) degrees
- \( r = 14 \) inches
Now substituting these values into the formula:
\[ L = \frac{42}{360} \times 2\pi \times 14 \]
Calculating step by step:
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Calculate \( \frac{42}{360} \): \[ \frac{42}{360} = 0.11667 \quad (\text{approximately}) \]
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Calculate \( 2\pi \): \[ 2\pi \approx 6.2832 \]
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Combine these results: \[ L \approx 0.11667 \times 6.2832 \times 14 \]
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Calculate \( 6.2832 \times 14 \): \[ 6.2832 \times 14 \approx 87.967 \]
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Finally, multiply by \( 0.11667 \): \[ L \approx 0.11667 \times 87.967 \approx 10.27 \text{ inches} \]
Rounding to the nearest inch, the length of the arc is approximately:
\[ \boxed{10} \text{ inches} \]