Question 684424
You use the law of cosines actually to find the length of 'a'


a^2 = b^2 + c^2 - 2*b*c*cos(A)


a^2 = 12^2 + 9^2 - 2*12*9*cos(105)


a^2 = 225 - 216*cos(105)


a^2 = 225 - 216*(-0.258819)


a^2 = 280.904904


a = sqrt(280.904904)


a = 16.76021789


Now that you know that 


a = 16.76021789
b = 12
c = 9


You can use the law of sines to find angles B and C. I'll show you how to find angle B and I'll let you find angle C


sin(B)/b = sin(A)/a


sin(B)/12 = sin(105)/16.76021789


sin(B)/12 = 0.9659258/16.76021789


sin(B)/12 = 0.0576321


sin(B) = 12*0.0576321


sin(B) = 0.6915852


B = arcsin(0.6915852)


B = 43.7557225


So the angle B is roughly 43.7557225 degrees


I'll let you find angle C


Note: there are 2 ways to find angle C, you can use the fact that A+B+C = 180 (ie all angles must add to 180) or you can use the law of sines again.