1. **State the problem:** Find $\sin(B)$ for a right triangle where the vertical side is $\sqrt{13}$, the horizontal side is 6, and the hypotenuse is 7. Angle $B$ is between the vertical side and the hypotenuse. 2. **Recall the sine definition:** For any angle in a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$. 3. **Identify the opposite side to angle $B$:** Since $B$ is between the vertical side ($\sqrt{13}$) and the hypotenuse (7), the side opposite $B$ is the horizontal side, which is 6. 4. **Apply the formula:** $$\sin(B) = \frac{6}{7}$$ 5. **Conclusion:** The sine of angle $B$ is $\frac{6}{7}$.