Find arc length of 130 degrees r=3 inch

1 answer

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:

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