1. **Problem statement:** Find $\tan(\beta)$ in the right triangle with sides 8, 15, and 17, where $\beta$ is the angle at vertex B. 2. **Recall the definition:** In a right triangle, $\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}$. 3. **Identify sides relative to angle $\beta$:** - Opposite side to $\beta$ is side AC = 15. - Adjacent side to $\beta$ is side BC = 8. 4. **Calculate $\tan(\beta)$:** $$\tan(\beta) = \frac{15}{8}$$ 5. **Answer:** The correct choice is A: $\frac{15}{8}$.