Is there a Pythagorean triple (a.k.a. an integer triangle) whose angles are 90, 45 and 45 degrees? I am trying to connect LEGO roads at angles other than the standard 90 degrees.
[Math] Pythagorean triple whose angles are 90, 45, and 45 degrees
geometrypythagorean triples
Best Answer
You cannot have an integer Pythagorean Triple whose angles are $45°, 45°$ and $90°$.
Assume on the triangle we have sides $a$. Then by Pythagoras' Theorem,
$$a^2+a^2=2a^2=(a\sqrt{2})^2$$
This means the hypotenuse is no longer an integer length, because now it measures $a\sqrt2$. This means no such Pythagoren Triple exists.