1. **State the problem:** Find $\sin(B)$ for a right triangle where the side opposite angle $B$ is $\sqrt{13}$, the adjacent side is $6$, and the hypotenuse is $7$. 2. **Recall the formula:** Using SOHCAHTOA, $\sin(B) = \frac{\text{opposite}}{\text{hypotenuse}}$. 3. **Substitute values:** $$\sin(B) = \frac{\sqrt{13}}{7}$$ 4. **Check if the triangle is valid:** Verify using Pythagoras theorem: $$6^2 + (\sqrt{13})^2 = 36 + 13 = 49 = 7^2$$ The triangle is valid. 5. **Final answer:** $$\sin(B) = \frac{\sqrt{13}}{7}$$ This is the exact value of $\sin(B)$ for the given triangle.