Triangles...

[Larsson]

Is it possible to have a non-Pythagorean triangle, and if it is, how does it look?

[Pete]

Any triangle not having any angle as a right angle is non-Pythgorean. Try one with sides 5,5,8

[spiffo]

Further to what Pete said, don't forget that the SIN, COS and TAN rules are just a more complicated version of Pythagoras' theorum (it's true. Put 90 degrees into the equations and you'll probably see what I mean), but they work even if there aren't any right angles. Also, remember that any non-right-angled triangle can be broken into right-angled triangles. For instance, imagine a tall isoscolese (sorry if the spelling's wrong) triangle with a thin base. Draw a verticle line from the top corner to the middle of the base. Look! You've got two right-angled triangles!

[rut]

All triangles are Pythagorean. It is impossible to have one which does not follow the theorem. However right angled triangles only follow the simple version of it.