I am a little lost. If everything you typed in a) is what you wished type then there is only one triangle possible. Unless there is an equal sign somewhere that shouldn't be there;

A+B+C = 180°

Using the law of sines;

sin40°/35 = sinB/40

B = arcsin(40sin40°/35) ≈ 47.2746°

If C = 40° and B ≈ 47.2746°, then A ≈ 92.7254°

A = 92.7254°, a = 54.388

B = 47.2746°, b = 40

C = 40°, c = 35

Nothing else is possible unless C, c, or b are allowed to vary.