\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usetikzlibrary{shapes, calc, decorations} 
\usepackage{amsmath,amssymb}

\begin{document}
\begin{preview}
\begin{tikzpicture}[thick]
    \newcommand\XC{4}
    \newcommand\ALPHA{30}

    \newcommand\XB{{(\XC*(cos(\ALPHA)*cos(\ALPHA) - sin(\ALPHA)*sin(\ALPHA)) + \XC)*0.5}}
    \newcommand\YB{{sqrt(cos(\ALPHA)*\XC*cos(\ALPHA)*\XC - (\XC*(cos(\ALPHA)*cos(\ALPHA) - sin(\ALPHA)*sin(\ALPHA)) + \XC)*0.5*(\XC*(cos(\ALPHA)*cos(\ALPHA) - sin(\ALPHA)*sin(\ALPHA)) + \XC)*0.5)}}

    % Draw the triangle
    \draw[fill=gray!10]  (0,    0) coordinate (A) 
        -- (\XB,\YB) coordinate (C) 
        -- (\XC,  0) coordinate (B) 
        -- (0,    0);

    % Draw nodes
    \node at (A)[anchor=north] {A};
    \node at (B)[anchor=north] {B};
    \node at (C)[anchor=south] {C};

    % Draw edge text
    \node (c) at ($(A)!0.5!(B)$) [below] {c};
    \node (b) at ($(A)!0.5!(C)$) [above] {b};
    \node (a) at ($(B)!0.6!(C)$) [right] {a};


    % draw alpha
    \draw[fill=green!30] (0,0) -- (0:0.75cm) arc (0:\ALPHA:.75cm);
    \coordinate[label=right:$\alpha$] (Alpha) at (0.25,0.15);

    % draw beta
    \begin{scope}[shift={(\XC, 0)}]
        \draw[fill=red!30] (0,0) -- (-180:0.50cm) arc (180:{180-(90-\ALPHA)}:0.5cm);
        \draw (150:0.35cm) node {$\beta$};
    \end{scope}

    % draw gamma
    \begin{scope}[shift={(\XB, \YB)}]
        \draw[fill=blue!30] (0,0) -- ({180+\ALPHA}:0.5cm) arc ({180+\ALPHA}:{180+\ALPHA+90}:0.5cm);
        \draw (-0.1, -0.05) node[below] {$\gamma$};
    \end{scope}

    \draw  (0,    0) coordinate (X) 
        -- (\XB,\YB) coordinate (Y) 
        -- (\XC,  0) coordinate (Z) 
        -- (0,    0);
\end{tikzpicture}
\end{preview}
\end{document}
