1. Proving

"Right Spherical Triangle"

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

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?

2. Ok I'm wrong. Already look at the answer on the book.
so A = 180 - 120 = 60
> I subtracted 120/100 from 180, because I need to choose the shortest arc length.
a = 180 - 100 = 80

I should use sinb = tana*cotA

log sinb = log tana*cotA
log sinb = log tana + log cotA

log tana = .75368
log cotA = 9.76144 - 10

log sinb = 0.51512
sinb = 3.27431155
so b = impossible

therefore: no solution

My question is: Why do I have to use log?