1. **Problem statement:** We have a triangle with angles 44° and 60°, and a side of length 11 cm opposite the 44° angle. We need to find the length $x$ opposite the 60° angle. 2. **Formula used:** We use the Law of Sines, which states: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a$, $b$, and $c$ are sides opposite angles $A$, $B$, and $C$ respectively. 3. **Identify known values:** - Side $a = 11$ cm opposite angle $A = 44^\circ$ - Angle $B = 60^\circ$ - Side $b = x$ opposite angle $B$ 4. **Find the third angle:** $$C = 180^\circ - 44^\circ - 60^\circ = 76^\circ$$ 5. **Apply Law of Sines:** $$\frac{11}{\sin 44^\circ} = \frac{x}{\sin 60^\circ}$$ 6. **Solve for $x$:** $$x = \frac{11 \times \sin 60^\circ}{\sin 44^\circ}$$ 7. **Calculate sine values:** $$\sin 60^\circ \approx 0.8660$$ $$\sin 44^\circ \approx 0.6947$$ 8. **Calculate $x$:** $$x = \frac{11 \times 0.8660}{0.6947} \approx \frac{9.526}{0.6947} \approx 13.71$$ 9. **Round to 2 significant figures:** $$x \approx 14$$ cm **Final answer:** The length $x$ is approximately 14 cm to 2 significant figures.