Theo công thức tính diện tích tam giác ta có:
\(\begin{array}{l}
{S_{ABC}} = \dfrac{1}{2}ab\sin C = \dfrac{1}{2}ac\sin B = \dfrac{1}{2}bc\sin A\\
\Leftrightarrow \left\{ \begin{array}{l}
ab\sin C = ac\sin B\\
ab\sin C = bc\sin A
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
\dfrac{b}{{\sin B}} = \dfrac{c}{{\sin C}}\\
\dfrac{c}{{\sin C}} = \dfrac{a}{{\sin A}}
\end{array} \right.\\
\Rightarrow \dfrac{a}{{\sin A}} = \dfrac{b}{{\sin B}} = \dfrac{c}{{\sin C}}.
\end{array}\)
