Properties Of Triangles

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

a = 2R \sin A,\quad b = 2R \sin B,\quad c = 2R \sin C

a^2 = b^2 + c^2 - 2bc \cos A

\cos A = \frac{b^2 + c^2 - a^2}{2bc}

b^2 = c^2 + a^2 - 2ca \cos B

c^2 = a^2 + b^2 - 2ab \cos C

a = b \cos C + c \cos B

b = c \cos A + a \cos C

c = a \cos B + b \cos A

\sin \frac{A}{2} = \sqrt{\frac{(s-b)(s-c)}{bc}}

\cos \frac{A}{2} = \sqrt{\frac{s(s-a)}{bc}}

\tan \frac{A}{2} = \sqrt{\frac{(s-b)(s-c)}{s(s-a)}}

\Delta = \sqrt{s(s-a)(s-b)(s-c)}

\Delta = \frac{1}{2} bc \sin A