1. **State the problem:** We need to find the ratio that represents $\cos(\angle W)$ in the given right triangle. 2. **Recall the definition of cosine in a right triangle:** $$\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$$ where $\theta$ is the angle in question. 3. **Identify the sides relative to $\angle W$:** - The hypotenuse is given as 17. - The side adjacent to $\angle W$ is 15. - The side opposite $\angle W$ is 8. 4. **Apply the cosine formula:** $$\cos(\angle W) = \frac{15}{17}$$ 5. **Conclusion:** The ratio representing $\cos(\angle W)$ is $\frac{15}{17}$.