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?