To find the arc length of a circle given an angle in degrees and the radius, you can use the formula:
\[ L = \frac{\theta}{360} \times 2\pi r \]
where:
- \(L\) is the arc length,
- \(\theta\) is the angle in degrees,
- \(r\) is the radius of the circle.
In this case:
- \(\theta = 130\) degrees,
- \(r = 3\) inches.
Now, plug the values into the formula:
\[ L = \frac{130}{360} \times 2\pi \times 3 \]
First, simplify \(\frac{130}{360}\):
\[ \frac{130}{360} = \frac{13}{36} \]
Now, substitute this back into the formula:
\[ L = \frac{13}{36} \times 2\pi \times 3 \]
This simplifies to:
\[ L = \frac{13}{36} \times 6\pi = \frac{78\pi}{36} = \frac{13\pi}{6} \]
Now, if you want a numerical approximation, you can use \(\pi \approx 3.14\):
\[ L \approx \frac{13 \times 3.14}{6} = \frac{40.82}{6} \approx 6.80 \text{ inches} \]
Thus, the arc length is:
\[ L = \frac{13\pi}{6} \text{ inches} \approx 6.80 \text{ inches} \]