Line-plane angles are complementary to the angle between any normal vector of a line and a plane, so the sine of a line-plane angle is equal to the cosine of the normal vector of the line and the normal vector of the plane.

The dihedral angle is equal to the angle between the normal vectors of the two corresponding planes, so the cosine of the dihedral angle is equal to the cosine of the corresponding normal vectors of the two planes.

(One in, one out, note whether the angle is acute or obtuse.)