Pythagorean theorem and special right triangles

[yo4561]

These are elementary triangle questions, but to confirm my understanding:

-Could right triangles have angles other than 45-45-90 and 30-60-90 (e.g. can you have a 90-50-40) etc.?

-For common right triangles, do we know anything about the angles? (e.g. do the sides 3-4-5 tell you anything about the other angles besides the 90 degree angle)?

Thank you in advance!

[esledge]

-Could right triangles have angles other than 45-45-90 and 30-60-90 (e.g. can you have a 90-50-40) etc.?

Yes! As long as the three angles sum to 180, it's a valid triangle. And as long as one of them is exactly 90, it's a valid right triangle. So you could even have a 1-89-90 (it would be very pointy and skinny) or a 44.3-45.7-90 (it would look almost like a 45-45-90, but wouldn't exactly be...this is why we don't just trust how pictures appear, and demand labels or written info to reach such conclusions).

-For common right triangles, do we know anything about the angles? (e.g. do the sides 3-4-5 tell you anything about the other angles besides the 90 degree angle)?

For the Pythagorean Triples with integer side lengths, none of the angles are nice, integer numbers except 90. You'd need a calculator and trigonometry rules to solve for those angles, so the GMAT doesn't get into that.