Answer
The arc length is $\frac{20\pi }{5}\text{ inches or }20.94\,\text{inches}$
Work Step by Step
We know that the formula which connects the arc length $s$, the angle intercepted by the arc to the center of the circle $\theta $, and the radius of the circle or arc $r$ is:
$s=r\theta $
Where $\theta $ is expressed in radians. To convert the angle mentioned in degrees to radians, multiply the angle in degree with $\frac{\pi }{180}.$
In the provided problem, r is 8 inches and the angle that is intercepted by the arc is 150 degrees.
When converting the angle in degree to radians:
$\begin{align}
& \theta =150{}^\circ \times \frac{\pi }{180}\text{ radians} \\
& =\frac{5\pi }{6}\text{ radians}
\end{align}$
So, the length of the arc is:
$\begin{align}
& s=r\theta \\
& =8\times \frac{5\pi }{6} \\
& =\frac{20\pi }{3}\text{ inches}\text{.}
\end{align}$
Round off the length value to two decimal places;
$\frac{20\pi }{3}\text{ inches}\approx \text{20}\text{.94 inches}\text{.}$
