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