Guide to Game Development/Theory/Mathematics/Trigonometry/Trigonometry used with non-right angles

An example of a triangle with sides a, b and c and with angles A, B and C.

For non-right-angled triangles, there are two rules that you can use:

Sine Rule -

For finding sides:
${\frac {a}{\sin(A)}}={\frac {b}{\sin(B)}}={\frac {c}{\sin(C)}}$

Rearranged for finding angles:
${\frac {\sin(A)}{a}}={\frac {\sin(B)}{b}}={\frac {\sin(C)}{c}}$

Cosine Rule -

For finding sides:
$a^{2}=b^{2}+c^{2}-2bc\cos(A)$
$b^{2}=a^{2}+c^{2}-2ac\cos(B)$
$c^{2}=a^{2}+b^{2}-2ab\cos(C)$

Rearranged for finding angles:
$\cos(A)={\frac {b^{2}+c^{2}-a^{2}}{2bc}}$

$\cos(B)={\frac {a^{2}+c^{2}-b^{2}}{2ac}}$

$\cos(C)={\frac {a^{2}+b^{2}-c^{2}}{2ab}}$