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.