1. **Stating the problem:** We are given that triangles $\triangle TUS$ and $\triangle VWS$ are similar, denoted as $\triangle TUS \sim \triangle VWS$. We need to find which ratio is equivalent to $\cos \angle U$ in the diagram. 2. **Recall the cosine definition:** For any angle in a right triangle, $\cos \theta = \frac{\text{adjacent side}}{\text{hypotenuse}}$. 3. **Identify $\angle U$ in $\triangle TUS$:** The angle $U$ is at vertex $U$ in $\triangle TUS$. The side adjacent to $\angle U$ is $\overline{US}$, and the hypotenuse is $\overline{UT}$. 4. **Write the cosine ratio for $\angle U$ in $\triangle TUS$:** $$\cos \angle U = \frac{US}{UT}$$ 5. **Use similarity to find equivalent ratio in $\triangle VWS$:** Since $\triangle TUS \sim \triangle VWS$, corresponding sides are proportional: $$\frac{US}{UT} = \frac{WS}{VW}$$ 6. **Conclusion:** The ratio equivalent to $\cos \angle U$ is $$\cos \angle U = \frac{US}{UT} = \frac{WS}{VW}$$ Thus, the ratio $\frac{WS}{VW}$ in $\triangle VWS$ is equivalent to $\cos \angle U$ in $\triangle TUS$.