1. **State the problem:** We have a right triangle $\triangle TUV$ with $\angle V = 90^\circ$, sides $UT = 5$, $VU = 4$, and $TV = 3$. We need to find $\cos(\angle U)$ to the nearest hundredth. 2. **Recall the cosine definition:** In a right triangle, $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$. 3. **Identify the sides relative to $\angle U$:** - The hypotenuse is $UT = 5$. - The side adjacent to $\angle U$ is $VU = 4$. 4. **Calculate $\cos(\angle U)$:** $$\cos(\angle U) = \frac{VU}{UT} = \frac{4}{5}$$ 5. **Simplify and approximate:** $$\frac{4}{5} = 0.8$$ 6. **Final answer:** $\cos(\angle U) = 0.80$ to the nearest hundredth.