Question

Find arc length of 130 degrees r=3 inch

Answer 1

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:

\[
L = \frac{13\pi}{6} \text{ inches} \approx 6.80 \text{ inches}
\]