1. **State the problem:** We are given a triangle ABC with angles $A=98.4^\circ$, $B=24.6^\circ$, and side $c=376$ opposite angle $C$. We need to find side $x$ opposite angle $B$ using the Law of Sines. 2. **Find angle $C$:** The sum of angles in a triangle is $180^\circ$. So, $$C = 180^\circ - A - B = 180^\circ - 98.4^\circ - 24.6^\circ = 57^\circ.$$ 3. **Law of Sines formula:** $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a$, $b$, and $c$ are sides opposite angles $A$, $B$, and $C$ respectively. 4. **Apply Law of Sines to find $x$ (side $b$):** $$\frac{x}{\sin 24.6^\circ} = \frac{376}{\sin 57^\circ}$$ 5. **Solve for $x$:** $$x = \frac{376 \times \sin 24.6^\circ}{\sin 57^\circ}$$ 6. **Calculate sine values:** $$\sin 24.6^\circ \approx 0.4161, \quad \sin 57^\circ \approx 0.8387$$ 7. **Compute $x$:** $$x = \frac{376 \times 0.4161}{0.8387} \approx \frac{156.45}{0.8387} \approx 186.5$$ **Final answer:** The side $x$ opposite angle $B$ is approximately $186.5$ units.