I want to know the triangles which satisfies the following equation :
$\sin^2 A + \sin^2 B = \sin C$. Here $A$, $B$, $C$ are angles of a triangle.
If we let $a$, $b$, $c$ to be the lengths of edges corresponded to angles, then we multiply $(abc)^2$ in the above equation. So we can conclude that $C$ is not larger strictly than $\pi/2$
So problem is divided into two cases without a loss of generality
Case 1 : $A$, $B < \pi/2$. This case is easy. Simple computation shows that $C = \pi/2$
Case 2 : $A > \pi/2$ and $B < \pi/2$
In this case I got one solution : $B=C$ so that sin(C) is a root of the equation $4t^2 +4t-1=0$
So I have a question : Can we solve this case in general ?