1. **State the problem:** We need to find the missing side length $x$ (side AB) in triangle ABC, where side AC = 3.2, angle B = 44.1°, and angle C = 58°. 2. **Find the missing angle A:** The sum of angles in a triangle is 180°. $$A = 180^\circ - 44.1^\circ - 58^\circ = 77.9^\circ$$ 3. **Use the Law of Sines:** The Law of Sines states: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a$, $b$, and $c$ are sides opposite angles $A$, $B$, and $C$ respectively. 4. **Assign sides:** Side AC = 3.2 is opposite angle B (44.1°), side AB = $x$ is opposite angle C (58°). 5. **Set up the ratio:** $$\frac{x}{\sin 58^\circ} = \frac{3.2}{\sin 44.1^\circ}$$ 6. **Solve for $x$:** $$x = \frac{3.2 \times \sin 58^\circ}{\sin 44.1^\circ}$$ 7. **Calculate sine values:** $$\sin 58^\circ \approx 0.8480$$ $$\sin 44.1^\circ \approx 0.6955$$ 8. **Substitute and compute:** $$x = \frac{3.2 \times 0.8480}{0.6955} = \frac{2.7136}{0.6955} \approx 3.9$$ **Final answer:** $$x \approx 3.9$$ (rounded to the nearest tenth)