1. **State the problem:** We need to find the ratio that represents $\tan(\angle W)$ in the right triangle with vertices $Q$, $B$, and $W$. The sides are given as $QB=8$, $BW=15$, and hypotenuse $QW=17$. 2. **Recall the definition of tangent in a right triangle:** $$\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}$$ where $\theta$ is the angle in question. 3. **Identify the sides relative to $\angle W$:** - The side opposite $\angle W$ is $QB = 8$. - The side adjacent to $\angle W$ is $BW = 15$. - The hypotenuse is $QW = 17$. 4. **Write the tangent ratio for $\angle W$:** $$\tan(\angle W) = \frac{\text{opposite}}{\text{adjacent}} = \frac{QB}{BW} = \frac{8}{15}$$ 5. **Conclusion:** The ratio representing $\tan(\angle W)$ is $\frac{8}{15}$. **Final answer:** $\boxed{\frac{8}{15}}$