I oriented my triangles with the side b along the horizontal (the initial side of angle A), and the side c as the terminal side. Then, drop a perpendicular line from the end of c down to the line that b sits on. It shouldn't take long for you to determine that the length of this vertical line is csin(A).
One of the fun things about proofs is knowing what you are allowed to assume and use. If you are allowed to use the well-known fact that the area of a triangle is 0.5*(base)*height) then you're essentially done.
If you can't use that as a known fact, then there is a little more work to do.