Zrjydtj

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] $sqrt1+x^2$~~~~~~~ (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
usepackageamsmath, amssymb, tikz

newcommandpythagwidth3cm
newcommandpythagheight2cm

begindocument
beginfigure[h]
centering

begintikzpicture[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] $sqrt1+x^2$~~~~~~~ (B) -- 
 node[right] ? (C) -- 
 node[below] ? 
 (A);
draw 
 (1.25cm,-1.0cm) rectangle (1.5cm,-0.75cm);

endtikzpicture
captionCaption
labelfig:my_label
endfigure
enddocument

Something like this? I use node[midway,above left=0pt,inner sep=0.5pt] $sqrt1+x^2$, where inner sep=0.5pt controls the distance.

documentclass[hidelinks,14pt, letterpaper]extarticle
usepackageamsmath, amssymb, tikz

newcommandpythagwidth3cm
newcommandpythagheight2cm

begindocument
beginfigure[h]
centering

begintikzpicture[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] $sqrt1+x^2$ (B) -- 
 node[right] ? (C) -- 
 node[below] ? 
 (A);
draw 
 (1.25cm,-1.0cm) rectangle (1.5cm,-0.75cm);

endtikzpicture
captionCaption
labelfig:my_label
endfigure
enddocument

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

documentclass[tikz,border=3.14mm]standalone
begindocument
begintikzpicture[scale=1.25]
draw (-1.5,-1) coordinate [label=left:$A$] (A) -- 
 node[midway,above,sloped] $sqrt1+x^2$ 
 (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);
endtikzpicture
enddocument

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

 documentclassarticle
usepackagepst-eucl%,
usepackageauto-pst-pdf

begindocument

 beginpostscript
 pssetunit=2, linejoin=1, PointSymbol=none,
 pstTriangle(-1.5,-1)A(1.5,1)B(1.5,-1)C
 ncline[linestyle=none]ABnaput*[nrot=:U]$ sqrt1 + x^2$
 pssetPointName=none
 pstMiddleABACIuput[d](I)?
 pstMiddleABBCJuput[r](J)?
 endpostscript

enddocument