Question 191537
a  sketch  would  help  but  bear  with  me

arc  =  120  deg  means  that  central  angle  bpa  =  120  deg

now  you  can  do  the  triangle  resolution  as  you  suggested

angle  pab  is  now  30  deg     (  (180-120)  /2  )  

pa  is  radius  =6

1/2  of  ba  is   sq  rt  of  (6^2 -3^2 )  =  5.196

ba  is  10.392

check  sin  60  deg  =  5.196 / 6  =  ,866        ok