SE-SKOLORNAS 1994 Problem 3

The vertex $B$ of the triangle $ABC$ lies in the plane $P$ . The plane of the triangle meets the plane in a line $L$ . The angle between $L$ and $AB$ is a, and the angle between $L$ and $BC$ is $b$ . The angle between the two planes is $c$ . Angle $ABC$ is $90^o$ . Show that $\sin^2c = \sin^2a + \sin^2b$ .