1. **State the problem:** We are given a circle with radius $r = 3$ meters and an angle $\theta = \frac{5\pi}{12}$ radians. We need to find the arc length corresponding to this angle. 2. **Formula for arc length:** The arc length $s$ of a circle is given by the formula: $$ s = r \times \theta $$ where $r$ is the radius and $\theta$ is the central angle in radians. 3. **Substitute the given values:** $$ s = 3 \times \frac{5\pi}{12} $$ 4. **Simplify the expression:** $$ s = \frac{3 \times 5\pi}{12} = \frac{15\pi}{12} $$ 5. **Reduce the fraction by canceling common factors:** $$ s = \frac{\cancel{15}\pi}{\cancel{12}} \to \frac{5\pi}{4} $$ 6. **Final answer:** The arc length is $$ s = \frac{5\pi}{4} \text{ meters} $$ This means the length of the arc subtended by the angle $\frac{5\pi}{12}$ radians on a circle of radius 3 meters is $\frac{5\pi}{4}$ meters.