1. **Problem statement:** Find $\sin(\alpha)$ in the given right triangle where $\alpha$ is the angle at vertex A. 2. **Recall the definition of sine in a right triangle:** $$\sin(\alpha) = \frac{\text{opposite side to } \alpha}{\text{hypotenuse}}$$ 3. **Identify the sides relative to angle $\alpha$:** - Opposite side to $\alpha$ is the side opposite vertex A, which is labeled 12. - Hypotenuse is the side opposite the right angle at C, labeled 37. 4. **Calculate $\sin(\alpha)$:** $$\sin(\alpha) = \frac{12}{37}$$ 5. **Conclusion:** The correct answer is option C: $\frac{12}{37}$.