1. **State the problem:** We need to find the length of side $x = UV$ in a right triangle $\triangle UTV$ where $\angle U = 90^\circ$, $UT = 64$, and $\angle T = 70^\circ$. 2. **Identify the sides relative to angle $T$:** - Side $UT = 64$ is adjacent to angle $T$. - Side $UV = x$ is opposite angle $T$. 3. **Use the tangent function:** The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 4. **Apply the formula:** $$\tan(70^\circ) = \frac{x}{64}$$ 5. **Solve for $x$:** $$x = 64 \times \tan(70^\circ)$$ 6. **Calculate the value:** Using a calculator, $$\tan(70^\circ) \approx 2.747$$ So, $$x \approx 64 \times 2.747 = 175.8$$ 7. **Final answer:** The length of side $UV$ is approximately **175.8** units.