I don't know the module, but some basic trig knowledge can help. In a right triangle, there is a simple relationship between angles and sides. If you have all three sides (SSS), then the following relationship holds true. Here's a diagram that demonstrates the SOH CAH TOA acronym. (sin = opposite/hypotenuse, cos = adjacant/hypotenuse, tan = opposite/adjacant). You could take this knowledge and create a routine that takes the sides in a specific order, calculates the sine values for the two unknown angles and then uses Math::Trig::asin() to get the angles. Seems quite long winded though :)

  A
  |\         sin A = a/b {(b is hypotenuse 4)
  | \        sin A = 3/5
  |  \
4 |   \ 5    sin C = c/b
  |    \     sin C = 4/5
  |90   \
  -------|
 B   3    C

Update: Not to mention that you only need to calculate one of the unknown angles to get all three. Since you have the 90 degrees, calculate one, then knowing that all 3 angles of a triangle have a sum of 180, you just subtract the two known angles from 180 and there's your third.

use strict;
use Math::Trig;
my @lengths = (3,4,5);
my @slengths = sort {$a <=> $b} @lengths;
my $a1 = atan($slengths[1]/$slengths[0]) * 180/3.141592653589;
my $a2 = 90 - $a1;
print "Angles are $a1, $a2\n";
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That's a nice solution. To comment on it a little, the sort finds the two shortest sides (so the hypotenuse is ignored). atan computes the the arctangent.

Math::Trig is bundled with perl, but if you wanted to use a builtin, you could use atan2 instead, passing the two sides as separate arguments.

That isn't as acurate a value of pi as possible. 3.14159265359 is closer (since the digits following 89 are 7932). You can use 4*atan2(1,1) to get a value with accuracy commensurate with your perl's floating point accuracy.

You can use 4*atan2(1,1) to get ... [pi]

Or, since atan2() is properly ranged from -pi to pi, you can use atan2(0,-1) and forego the multiplication

PerlJam

perldoc -f atan2
     atan2 Y,X
             Returns the arctangent of Y/X in the range -PI to
             PI.
 
             For the tangent operation, you may use the
             "Math::Trig::tan" function, or use the familiar
             relation:
 
                 sub tan { sin($_[0]) / cos($_[0])  }
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bash-2.03$ cat ./atan2.pl 
#!/usr/local/bin/perl -w
use strict;
 
my $x = defined($_=shift) ? $_ : die "Enter X\n";
my $y = defined($_=shift) ? $_ : die "Enter Y\n";
 
my $r = atan2( $y, $x );
print "angle = $r radians\n";
bash-2.03$ ./atan2.pl 4 3 
angle = 0.643501108793284 radians
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If it's expecting references, maybe my $ang = vecang(\@p,\@q);?
the forward slashes pass the arrays by reference. see perlref and perlreftut for details.