Formulas and reference

Sum of angles in a triangle

\[\alpha+\beta+\gamma=180^\circ\]

Semiperimeter of a triangle

\[p=\frac{a+b+c}{2}\]

Triangle area from a side and altitude

\[S=\frac12ah_a\]

Triangle area from two sides and the included angle

\[S=\frac12bc\sin\alpha\]

Heron's formula

\[S=\sqrt{p(p-a)(p-b)(p-c)}\]

Law of cosines

\[a^2=b^2+c^2-2bc\cos\alpha\]

Law of sines

\[\frac a{\sin\alpha}=\frac b{\sin\beta}=\frac c{\sin\gamma}=2R\]