What's the chance of an acute triangle?

[nuzzle]

But, is there some property of these sets that would enable as to quantify the relation between a set of all triangles and it's subset of acute triangles? Does mathematics define such a property? Something that would enable as to speak of these sets in a fashion similar to "percentage"? A numerical value that can tell us in more detail how one set relates to the other, enabling us to know more than just the fact that one is a subset of the other?

I was pretty convinced there existed a percentage of acute triangles among all triangles in the infinite plane, but arguments in this thread has lead me to believe that may not be the case. At least to be able to calculate the percentage you need to transform all triangles to the finite plane and by doing that you influence the percentage. I though I had found a transform which would keep the percentage intact but appearantly that's not even possible.

This is disturbing and my belief is that if you "instead of taking triangles to finity took probability to infinity" you could find the one true percentage. Maybe some matematician can figure that out but I can't.