1. **State the problem:** We have a triangle with one side length 5, and two angles 46° and 29°. We want to find the length of side $x$ using the Law of Sines. 2. **Recall the Law of Sines formula:** $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a$, $b$, $c$ are sides opposite angles $A$, $B$, $C$ respectively. 3. **Find the third angle:** The sum of angles in a triangle is 180°. $$C = 180^\circ - 46^\circ - 29^\circ = 105^\circ$$ 4. **Assign known values:** Let side opposite 46° be 5, side opposite 29° be $x$, and opposite 105° be $c$ (unknown and not needed here). 5. **Set up the Law of Sines ratio:** $$\frac{5}{\sin 46^\circ} = \frac{x}{\sin 29^\circ}$$ 6. **Solve for $x$:** $$x = \frac{5 \times \sin 29^\circ}{\sin 46^\circ}$$ 7. **Calculate sine values:** $$\sin 29^\circ \approx 0.4848, \quad \sin 46^\circ \approx 0.7193$$ 8. **Substitute and simplify:** $$x = \frac{5 \times 0.4848}{0.7193} = \frac{2.424}{0.7193}$$ 9. **Final calculation:** $$x \approx 3.37$$ **Answer:** The length of side $x$ is approximately 3.37.