Answer:
The exact value of the arc length is [tex]12.5\pi \ inches[/tex]
or
The approximately value of the arc length is [tex]39.27\ inches[/tex]
Step-by-step explanation:
we know that
By proportion
[tex]\frac{central\ angle}{2\pi}=\frac{arc\ length}{2\pi r}[/tex]
in this problem we have
[tex]central\ angle=\frac{5\pi}{6}[/tex]
[tex]r=15\ inches[/tex]
substitute the values
[tex]\frac{\frac{5\pi}{6}}{2\pi}=\frac{arc\ length}{2\pi (15)}\\ \\\frac{5\pi}{12\pi} =\frac{arc\ length}{30\pi} \\ \\ arc\ length=30\pi *(5/12)\\ \\arc\ length=12.5\pi \ inches[/tex]
[tex]arc\ length=39.27\ inches[/tex]
