Answer:
The arc length is;
[tex]\frac{5\pi}{3}\text{ in}[/tex]
Explanation:
Given that the central angle of the arc is;
[tex]\theta=\frac{\pi}{6}[/tex]
Recall that the formula for the length of an arc is;
[tex]\begin{gathered} l=\frac{\theta}{360}\times2\pi r=\frac{\theta}{2\pi}\times2\pi r=\theta r \\ \theta\text{ (in rad)} \end{gathered}[/tex]
substituting the central angle and radius;
[tex]\begin{gathered} l=\theta r=\frac{\pi}{6}\times10 \\ l=\frac{5}{3}\pi\text{ in} \end{gathered}[/tex]
Therefore, the arc length is;
[tex]\frac{5\pi}{3}\text{ in}[/tex]
