law of cosines

The law of cosines is a generalization of the Pythagorean theorem.

For a triangle with sides $a, b, c$ and respective opposite angles $α, β, γ$ ,

\begin{aligned} a^{2} & = b^{2} + c^{2} - 2 b c \cos α \\ b^{2} & = a^{2} + c^{2} - 2 a c \cos β \\ c^{2} & = a^{2} + b^{2} - 2 a b \cos γ \end{aligned}

\documentclass[tikz,margin={2cm 0cm}]{standalone}
\usepackage{tkz-euclide}
%
\begin{document}
\begin{tikzpicture}[scale=1.5]
    \tkzDefPoint(0,0){O}
    % \a must be the longest side!
    \def\a{4}
    \def\b{2}
    \def\c{3}
    \def\scale{1}
    \pgfmathsetmacro\angle{acos((\a^2+\b^2-\c^2)/(2*\a*\b))}
    %
    \tkzDefPoint(0:\scale*\a){A}
    \tkzDefPoint(\angle:\scale*\b){B}
    %
    \tkzMarkAngle[size=0.5](A,O,B)
		\tkzLabelAngle[pos=0.6](A,O,B){$\gamma$}
	\tkzMarkAngle[size=0.5](B,A,O)
		\tkzLabelAngle[pos=0.6](B,A,O){$\beta$}
	\tkzMarkAngle[size=0.5](O,B,A)
		\tkzLabelAngle[pos=0.6](O,B,A){$\alpha$}
	%
    \tkzDrawSegment[very thick](O,A)
        \tkzLabelSegment[below](O,A){$a$}
    \tkzDrawSegment[very thick](O,B)
        \tkzLabelSegment[above left](O,B){$b$}
    \tkzDrawSegment[very thick](B,A)
        \tkzLabelSegment[above right](B,A){$c$}
    %
    % \tkzDrawPoints(O,A,B)
\end{tikzpicture}
\end{document}