From the picture, we can tell that arc IJ has a central angle of 160° and that the circle has a diameter of 14 cm, or a radius of 7 cm.
Remember that the formula for arc length is:
[tex]L = r\theta[/tex]
- [tex]r[/tex] is the radius of the arc
- [tex]\theta[/tex] is the central angle (in radians)
We are almost able to find the arc length, but 160° is not in radians, which it has to be in order for us to properly use the formula. In order to convert it to radians, multiply the degree measure by [tex]\dfrac{\pi}{180}[/tex].
[tex]160^{\circ} = 160 \cdot \dfrac{\pi}{180}[/tex]
[tex]160^{\circ} = \dfrac{8\pi}{9}[/tex]
Now, we can use the formula:
[tex]L = 7 \cdot \dfrac{8\pi}{9} = \dfrac{56\pi}{9} \approx 19.55[/tex]
The answer is approximately 19.55.
