1. **Problem statement:** We are given a triangle with side BC = 376, angle A = 98.4°, and angle B = 24.6°. We need to find side AB = x using the Law of Sines. 2. **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. 3. **Find angle C:** Sum of angles in a triangle is 180°: $$C = 180^\circ - A - B = 180^\circ - 98.4^\circ - 24.6^\circ = 57^\circ$$ 4. **Assign sides:** - Side $a = BC = 376$ opposite angle $A = 98.4^\circ$ - Side $b = AB = x$ opposite angle $B = 24.6^\circ$ 5. **Apply Law of Sines to find $x$:** $$\frac{x}{\sin 24.6^\circ} = \frac{376}{\sin 98.4^\circ}$$ 6. **Solve for $x$:** $$x = \frac{376 \times \sin 24.6^\circ}{\sin 98.4^\circ}$$ Calculate sine values: $$\sin 24.6^\circ \approx 0.4161, \quad \sin 98.4^\circ \approx 0.9903$$ 7. **Calculate $x$ numerically:** $$x \approx \frac{376 \times 0.4161}{0.9903} \approx \frac{156.45}{0.9903} \approx 158.0$$ **Final answer:** $$x \approx 158.0$$