Triangle isocèle

\documentclass[12pt,border=5pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usetikzlibrary{calc,angles,quotes,positioning,decorations.markings,arrows.meta,patterns,intersections,shapes,trees}
\usepackage{amsmath,amssymb}
\begin{document}
\begin{tikzpicture}

    \node[isosceles triangle, isosceles triangle apex angle=44,draw,
        inner sep=0pt,anchor=lower side,rotate=90,draw=black,
        line width=1.5pt, minimum height=4cm, fill=gray!2] (triangle) at (1.6,-0.05) {};

    \draw[fill=green!30] (0,0) -- (0:0.50cm) arc (0:68:.50cm);
    \begin{scope}[shift={(3.2cm,0cm)}]
        \draw[fill=green!30] (0,0) -- (-180:0.50cm) arc (180:110:0.5cm);
        \draw (150:0.35cm) node {$\beta$};
    \end{scope}

    \begin{scope}[shift={(1.6cm,4cm)}]
        \draw[fill=red!30] (0,0) -- (250:.75cm) arc (250:292:.75cm);
        \draw (-90:0.5cm) node {$\gamma$};
    \end{scope}

    \coordinate[label=left:$A$] (A) at (0,0);
    \coordinate[label=right:$B$] (B) at (3.2,0);
    \coordinate[label=above:$C$] (C) at (1.6,4);

    \coordinate[label=below:$c$](c) at ($ (A)!.5!(B) $);
    \coordinate[label=left:$b$](b) at ($ (A)!.5!(C) $);
    \coordinate[label=right:$a$](a) at ($ (B)!.5!(C) $);

    \node[isosceles triangle, isosceles triangle apex angle=44,draw,
        inner sep=0pt,anchor=lower side,rotate=90,draw=black,
        line width=1.5pt, minimum height=4cm] (triangle) at (1.6,-0.05) {};

    \coordinate[label=45:$\alpha$] (Alpha) at (A);
  \end{tikzpicture}
\end{document}