Why don't you first try to use the cosine law to solve for an angle and then make use of the sin law to solve for the remaining angles.
Cosine law
C^2 = A^2 + B^2 - 2AB(cos C)
Solve for cos C, and then take the inverse of the trig ratio to solve for the angle.
Then set up a proportion like you have done using the sin law and solve for another angle. Knowing the sum of all angles in a triangle add up to 180 degrees, we can easily solve for the remaining angle.