Construct a triangle given angle a, altitude of a, and the perimeter

I read How To Solve It by George Polya and went overboard solving one of the example problems: Construct a triangle given the vertex angle, the height of the vertex, and the perimeter.  Here is my solution in PDF. Please leave comments to correct any mistakes.  Here are the source files as tarball.

I created the figures with eukleides, a language devoted to plane geometry.  There is not a lot of documentation but hopefully my figure source files (in the above tar ball) can help you get the gist of it.  Eukleides produces very nice figures.  Create an EPS from the EUK file, then convert that with epstopdf to include it in the latex file.

$> eukleides FIGURE.euk
$> eps2topdf FIGURE.eps

I created the document in LaTeX, specifically the pdflatex package.