This answer may be more complicated than needed but here itis. First we need to set up a right triangle. The hypot. is 12in because that is the radius. second we know that one leg is 1 in use pyth. theor. to solve for third leg

\(\displaystyle{b}=\sqrt{{{12}^{{2}}-{1}^{{2}}}}=\sqrt{{{143}}}\)

now we can use tha law of sines to figure out theta

\(\displaystyle{\frac{{{\sin{{\left(\theta\right)}}}}}{{\sqrt{{{143}}}}}}={\frac{{{\sin{{\left({90}\right)}}}}}{{{12}}}}\)

So \(\displaystyle\theta={{\sin}^{{-{1}}}{\left({\sin{{\left({90}\right)}}}\cdot{\frac{{\sqrt{{{143}}}}}{{{12}}}}\right)}}\)

\(\displaystyle\theta\) is approximately \(\displaystyle{85.2}^{\circ}\)

Now we know theta is the central angle so we canb plug itinto the formula

\(\displaystyle\text{Arc Length}={\left({\frac{{\text{central angle}}}{{{360}^{\circ}}}}\right)}\cdot{2}\pi{r}\)

\(\displaystyle={\left({\frac{{{85.2}}}{{{360}^{\circ}}}}\right)}\cdot{2}\pi{12}\)

\(\displaystyle={17.844}\)

Second distance

\(\displaystyle{360}-{85.2}={274.8}\)

\(\displaystyle{\left({\frac{{{274.8}}}{{{360}}}}\right)}\cdot{2}\pi{12}={57.55}\)

This is the actual arc length.