Answer:
110.01 in
Step-by-step explanation:
To find the radius of a circle in which the central angle, α, intercepts an arc of the given length s, we can use the arc length formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Arc length}}\\\\s= 2\pi r\left(\dfrac{\alpha}{360^{\circ}}\right)\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$s$ is the arc length.}\\\phantom{ww}\bullet\;\textsf{$r$ is the radius.}\\\phantom{ww}\bullet\;\textsf{$\alpha$ is the central angle in degrees.}\end{array}}[/tex]
In this case:
Substitute the given values into the formula and solve for r:
[tex]96= 2\pi r\left(\dfrac{50^{\circ}}{360^{\circ}}\right)\\\\\\48= \pi r\left(\dfrac{5}{36}\right)\\\\\\48 \cdot \dfrac{36}{5}=\pi r\\\\\\345.6=\pi r\\\\\\r=\dfrac{345.6}{\pi}\\\\\\r=110.007896665...\\\\\\r=110.01\; \sf in\;(nearest\;hundredth)[/tex]
Therefore, the radius of the circle rounded to the nearest hundredth is:
[tex]\LARGE\boxed{\boxed{110.01\; \sf in}}[/tex]
