1. **State the problem:** We need to find the length $x = VU$ in the right triangle $\triangle VUT$ where $\angle U = 90^\circ$, $UT = 64$, and $\angle UTV = 70^\circ$. 2. **Identify known elements:** Since $\angle U$ is the right angle, $UT$ and $VU$ are legs, and $VT$ is the hypotenuse. 3. **Use trigonometric ratios:** The angle given is $\angle UTV = 70^\circ$, which is the angle at vertex $T$. The side opposite this angle is $VU = x$, and the side adjacent is $UT = 64$. 4. **Apply the tangent function:** $$\tan(70^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{x}{64}$$ 5. **Solve for $x$:** $$x = 64 \times \tan(70^\circ)$$ 6. **Calculate the value:** $$x = 64 \times 2.747477419 \, \approx 175.8$$ 7. **Final answer:** $$\boxed{175.8}$$ So, the length $VU$ rounded to the nearest tenth is $175.8$.