1. **State the problem:** We have triangle UVW with angles at V and W given as $110^\circ$ and $2.3^\circ$ respectively, and side UV = 6. We need to find side $v = UW$. 2. **Find the missing angle:** The sum of angles in a triangle is $180^\circ$. So, angle $U = 180^\circ - 110^\circ - 2.3^\circ = 67.7^\circ$. 3. **Use the Law of Sines:** The Law of Sines states $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a,b,c$ are sides opposite angles $A,B,C$ respectively. Here, side $UV=6$ is opposite angle $W=2.3^\circ$, and side $UW=v$ is opposite angle $V=110^\circ$. 4. **Set up the ratio:** $$\frac{v}{\sin 110^\circ} = \frac{6}{\sin 2.3^\circ}$$ 5. **Solve for $v$:** $$v = \frac{6 \times \sin 110^\circ}{\sin 2.3^\circ}$$ 6. **Calculate values:** $\sin 110^\circ \approx 0.9397$ $\sin 2.3^\circ \approx 0.0401$ 7. **Substitute:** $$v = \frac{6 \times 0.9397}{0.0401} = \frac{5.6382}{0.0401} \approx 140.6$$ **Final answer:** $$v \approx 140.6$$ Rounded to the nearest tenth, $v = 140.6$.