Định lí côsin và định lí sin

$\begin{array}{l}{a^2} = {b^2} + {c^2} - 2bc\cos A\\{b^2} = {c^2} + {a^2} - 2ca\cos B\\{c^2} = {a^2} + {b^2} - 2ab\cos C\end{array}$

$\begin{array}{l}\cos A = \dfrac{{{b^2} + {c^2} - {a^2}}}{{2bc}}\\\cos B = \dfrac{{{c^2} + {a^2} - {b^2}}}{{2ca}}\\\cos C = \dfrac{{{a^2} + {b^2} - {c^2}}}{{2ab}}\end{array}$

$\dfrac{a}{{\sin A}} = \dfrac{b}{{\sin B}} = \dfrac{c}{{\sin C}} = 2R$

$a = 2R\sin A$

$b = 2R\sin B$

$c = 2R\sin C$

1) $S = \dfrac{1}{2}a{h_a} = \dfrac{1}{2}b{h_b} = \dfrac{1}{2}c{h_c}$;

2) $S = \dfrac{1}{2}ab\sin C = \dfrac{1}{2}bc\sin A = \dfrac{1}{2}ac\sin B$;

3) $S = \dfrac{{abc}}{{4R}}$;

4) $S = pr$;

5) $S = \sqrt {p(p - a)(p - b)(p - c)}$ (công thức Heron).