The Law of Sines says
[tex]\dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c}[/tex]
[tex]\sin A = \dfrac a b \sin B[/tex]
[tex]A = \arcsin( \dfrac{782}{1435} \sin 115.6 ) = 29.44^\circ[/tex]
We don't have to worry about the obtuse supplement because a triangle can only have one obtuse angle, and that's B.
[tex]C = 180 - 115.6 - 29.44 = 34.96^\circ[/tex]
Answer: A=29.44°, C=34.96°
