One way to solve this problem is to use the Law of Sines: sin(A)/a = sin(B)/b = sin(C)/c. Here a, b, c are the lengths of the sides, and A, B, C are the angles across from (not touching) the sides a, b, c respectively.
Since you are given b, c, and B, you could plug them into sin(B)/b = sin(C)/c to find C. Having found C, use the fact that the angles of a triangle sum to 180 degrees to find A. Then plug A, B, and b into sin(A)/a = sin(B)/b to find a.
Hope this helps!