A circular sector has an area of $192 \mathrm{in}^{2}$. The radius of the circle is 8 in. What is the arc length of the sector?
The arc length of the sector is in.
(Type an integer or a decimal.)

Step 1 ：The area of a circular sector is given by the formula \(A = \frac{1}{2} r^2 \theta\), where \(r\) is the radius of the circle and \(\theta\) is the central angle in radians. We can rearrange this formula to solve for \(\theta\): \(\theta = \frac{2A}{r^2}\).

Step 2 ：The arc length of a sector is given by the formula \(s = r \theta\). Substituting the expression for \(\theta\) from above, we get \(s = r \cdot \frac{2A}{r^2} = \frac{2A}{r}\).

Step 3 ：We can plug in the given values \(A = 192 \mathrm{in}^{2}\) and \(r = 8 \mathrm{in}\) to find the arc length.

Step 4 ：Substituting the values into the formula, we get \(s = \frac{2 \times 192}{8} = 48.0\).

Step 5 ：Final Answer: The arc length of the sector is \(\boxed{48}\) inches.