Giải thích các bước giải:
Áp dụng: \(\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}}\) ta có:
\(\begin{array}{l}
1,\\
\frac{{AB}}{{\sin C}} = \frac{{AC}}{{\sin B}} = \frac{{BC}}{{\sin A}}\\
\Leftrightarrow \frac{{\sqrt 2 }}{{\sin 45^\circ }} = \frac{{\sqrt 3 }}{{\sin B}} = \frac{{BC}}{{\sin A}}\\
\Rightarrow \sin B = \frac{{\sqrt 3 }}{2} \Rightarrow \widehat B = 60^\circ \\
\Rightarrow \widehat A = 180^\circ - \widehat B - \widehat C = 75^\circ \\
\Rightarrow BC = \frac{{\sqrt 2 }}{{\sin 45^\circ }}.\sin A = \frac{{\sqrt 6 + \sqrt 2 }}{2}\\
2,\\
\widehat A = 180^\circ - \widehat B - \widehat C = 75^\circ \\
\frac{{AB}}{{\sin C}} = \frac{{AC}}{{\sin B}} = \frac{{BC}}{{\sin A}}\\
\Leftrightarrow \frac{5}{{\sin 45^\circ }} = \frac{{AC}}{{\sin 60^\circ }} = \frac{{BC}}{{\sin 75^\circ }}\\
\Rightarrow \left\{ \begin{array}{l}
AC = \frac{{5\sqrt 6 }}{2}\\
BC = \frac{{5 + 5\sqrt 3 }}{2}
\end{array} \right.
\end{array}\)
