I am assuming you want to measure angles in degrees - not in radians!As simple as the title says it. Is it possible to have a right triangle with 3 integer sides and 3 integer angles(30 degrees, 11 degrees, 79 degrees, etc.)
I would begin with a well-known method for generating Pythagorean triples:
[MATH](a,b,c)=(m^2-n^2,4mn,m^2+n^2)[/MATH] where \(m,n\in\mathbb{N}\) and \(n<m\)
And so, if you are using degrees to measure the angles, it will suffice to find an ordered pair \((m,n)\) such that:
[MATH]\frac{180}{\pi}\arctan\left(\frac{m^2-n^2}{4mn}\right)=k[/MATH] where \(k\in\mathbb{N}\) and \(k<90\).
I would likely use a computer to search for a solution.
Shouldn't there be a condition so that [math]m, n \neq 0[/math]?
That is implied with \(m,n\in\mathbb{N}\). The natural numbers are positive integers.