Question

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Question
If the central angle of a circle measures 42 degrees and the radius is 14 inches long, then how long is the arc intercepted to the nearest inch?(1 point)

Answer 1

To find the length of the arc intercepted by a central angle, you can use the formula:

\[
\text{Arc Length} = \frac{\theta}{360} \times 2\pi r
\]

where:
- \(\theta\) is the central angle in degrees,
- \(r\) is the radius of the circle.

In this case,
- \(\theta = 42\) degrees,
- \(r = 14\) inches.

Now, plug the values into the formula:

\[
\text{Arc Length} = \frac{42}{360} \times 2\pi \times 14
\]

First, calculate \(\frac{42}{360}\):

\[
\frac{42}{360} = \frac{7}{60} \approx 0.1167
\]

Now, calculate \(2\pi \times 14\):

\[
2\pi \times 14 \approx 28\pi \approx 87.96
\]

Now, multiply these together:

\[
\text{Arc Length} \approx 0.1167 \times 87.96 \approx 10.28
\]

Rounding to the nearest inch, the arc length is approximately:

\[
\text{Arc Length} \approx 10 \text{ inches}
\]

So, the length of the arc intercepted is **10 inches**.