1. **Problem:** Given a circle with radius $8$ m and central angle $45^\circ$, find the arc length. 2. **Formula:** The arc length $s$ of a circle is given by $$s = r \theta$$ where $r$ is the radius and $\theta$ is the central angle in radians. 3. **Convert degrees to radians:** $$\theta = 45^\circ = 45 \times \frac{\pi}{180} = \frac{\pi}{4}$$ 4. **Calculate arc length:** $$s = 8 \times \frac{\pi}{4} = 2\pi$$ 5. **Answer:** The arc length is $2\pi$ meters. This means the length of the arc subtended by a $45^\circ$ angle in a circle of radius $8$ m is $2\pi$ m.