1. **Problem Statement:** Find $\sin(\beta)$ in a right triangle with sides 3, 4, and 5, where the right angle is at vertex C and angle $\beta$ is at vertex B. 2. **Recall the definition of sine:** $$\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$$ 3. **Identify the sides relative to angle $\beta$:** - Opposite side to $\beta$ is 4. - Hypotenuse is the longest side, which is 5. 4. **Calculate $\sin(\beta)$:** $$\sin(\beta) = \frac{4}{5}$$ 5. **Conclusion:** The value of $\sin(\beta)$ is $\frac{4}{5}$. Therefore, the correct answer is D: $\frac{4}{5}$.