How long is an arc intercepted by the given central angle in a circle of radius $13.75 \mathrm{mi}$ ? $45^{\circ}$ The length of the intercepted arc is approximately \mathrm{mi}$. (Round to the nearest hundredth.)

Step 1 ：The problem is asking for the length of an arc intercepted by a central angle in a circle of radius 13.75 miles. The central angle is given as 45 degrees.

Step 2 ：The length of an arc in a circle can be calculated using the formula: \(\text{Arc length} = \left(\frac{\text{central angle}}{360}\right) \times 2\pi \times \text{radius}\)

Step 3 ：Substituting the given values into the formula, we get: \(\text{Arc length} = \left(\frac{45}{360}\right) \times 2\pi \times 13.75\)

Step 4 ：Solving the above expression, we find that the length of the intercepted arc is approximately 10.8 miles.

Step 5 ：\(\boxed{10.8}\) is the final answer.