"Right Spherical Triangle"

Prove: C = 90degrees, A = 120degrees, a = 100degrees

Answer is no solution

sin a = sin A * sin c

sin a = tan b * ctn B

sin b = sin B * sin c

sin b = tan a * ctn A

cos c = cos a * cos b

cos c = ctn A * ctn B

cos A = cos a * sin B

cos A = tan b * ctn c

cos B = cos b * sin A

cos B = tan a * ctn c

What I have done is this: so using sin a = sin A * sin c

sin100 = sin120 * sinc.....sinc = 1.137158043 so we know that it has no solution, because the range of sine is [-1,1] and sinc > 1.btw, is this correct? and if so, is this the right way to pove it?