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I managed to align my hypotenuse text with the hypotenuse side of my triangle, but I feel like it was done inefficiently using a lot of ~~~~~~ in this line node[above] {$sqrt{1+x^2}$~~~~~~~} (B) --.

Is there a better way to get the same alignment that I have now without the excessive use of ~?

documentclass[hidelinks,14pt, letterpaper]{extarticle}

usepackage{amsmath, amssymb, tikz}



newcommand{pythagwidth}{3cm}

newcommand{pythagheight}{2cm}



begin{document}

begin{figure}[h]

centering



begin{tikzpicture}[scale=1.25]

coordinate [label=left:$A$] (A) at (-1.5cm,-1.cm);

coordinate [label=above:$B$] (B) at (1.5cm,1.0cm);

coordinate [label=below right:$C$] (C) at (1.5cm,-1.0cm);

draw 

  (A) -- 

  node[above] {$sqrt{1+x^2}$~~~~~~~} (B) -- 

  node[right] {?} (C) -- 

  node[below] {?} 

  (A);

draw 

  (1.25cm,-1.0cm) rectangle (1.5cm,-0.75cm);



end{tikzpicture}

caption{Caption}

label{fig:my_label}

end{figure}

end{document}

Something like this? I use node[midway,above left=0pt,inner sep=0.5pt] {$sqrt{1+x^2}$}, where inner sep=0.5pt controls the distance.

documentclass[hidelinks,14pt, letterpaper]{extarticle}

usepackage{amsmath, amssymb, tikz}



newcommand{pythagwidth}{3cm}

newcommand{pythagheight}{2cm}



begin{document}

begin{figure}[h]

centering



begin{tikzpicture}[scale=1.25]

coordinate [label=left:$A$] (A) at (-1.5cm,-1.cm);

coordinate [label=above:$B$] (B) at (1.5cm,1.0cm);

coordinate [label=below right:$C$] (C) at (1.5cm,-1.0cm);

draw 

  (A) -- 

  node[midway,above left=0pt,inner sep=0.5pt] {$sqrt{1+x^2}$} (B) -- 

  node[right] {?} (C) -- 

  node[below] {?} 

  (A);

draw 

  (1.25cm,-1.0cm) rectangle (1.5cm,-0.75cm);



end{tikzpicture}

caption{Caption}

label{fig:my_label}

end{figure}

end{document}

ADDENDUM: Just for fun: an even simpler and shorter code with TikZ...

documentclass[tikz,border=3.14mm]{standalone}

begin{document}

begin{tikzpicture}[scale=1.25]

draw  (-1.5,-1) coordinate [label=left:$A$] (A) -- 

  node[midway,above,sloped] {$sqrt{1+x^2}$} 

  (1.5,1) coordinate [label=above:$B$] (B) --

  node[right] {?} 

  (1.5,-1)coordinate [label=below right:$C$] (C) -- 

  node[below] {?} cycle;

draw ([xshift=-0.25cm]C) |- ([yshift=0.25cm]C);

end{tikzpicture}

end{document}

Just for fun: with pstricks, a very short code to have this figure:

 documentclass{article}

usepackage{pst-eucl}%,

usepackage{auto-pst-pdf}



begin{document}



    begin{postscript}

    psset{unit=2, linejoin=1, PointSymbol=none,}

    pstTriangle(-1.5,-1){A}(1.5,1){B}(1.5,-1){C}

    ncline[linestyle=none]{A}{B}naput*[nrot=:U]{$ sqrt{1 + x^2}$}

    psset{PointName=none}

    pstMiddleAB{A}{C}{I}uput[d](I){?}

    pstMiddleAB{B}{C}{J}uput[r](J){?}

    end{postscript}



end{document}