Using law of sines:













∠C is an acute (QI) angle and ∠AC'B is an 
obtuse (QII) angle.  They have the same sine and are
supplementary.

Using the inverse sine feature of our calculator,

∠C = 67.44208077°

so ∠AC'B = 180°-67.44208077° = 112.5579192°

To find side AC and AC', we use the law of cosines:



Swap sides:



Rearrange terms and a factor with 0 on the right:







Use the quadratic formula





Using the + gives us AC = 6.575659859
Using the - gives us AC' = 3.353275637

We can find ∠ABC and ∠ABC' by adding the 
two angles we now know and subtracting from 180°.

You can finish that part.

Edwin