Answer
$x\approx318.76$
Work Step by Step
The triangle is shown in the attached image below.
Angles $A$ and $B$ are known. Since $\angle A+\angle B+\angle C=180^{\circ}$, substitute the known angles into the formula and solve for $\angle C$:
$\angle C=180^{\circ}-24.6^{\circ}-98.4^{\circ}=57^{\circ}$
Substitute the known values into the formula $\dfrac{\sin A}{a}=\dfrac{\sin C}{x}$, obtained from the Law of Sines and solve for $x$ to find the unknown side:
$\dfrac{\sin98.4^{\circ}}{376}=\dfrac{\sin57^{\circ}}{x}$
$\dfrac{376}{\sin98.4^{\circ}}=\dfrac{x}{\sin57^{\circ}}$
$x=\Big(\dfrac{\sin57^{\circ}}{\sin98.4^{\circ}}\Big)376\approx318.76$
