Other than the dubious inverse cosine number, the rest of your process looks like exactly what I did. I'm not entirely sure I'm right either, but my method is the same as yours, for whatever that's worth.As we know, PF = 80%.
Apparent power is VA = 100V * 20A = 2000W.
True Power being 80% of Apparent Power = 1600W
acos(0.80) = 38.659808254090090604005862335173° (phase angle)
1st Phasor: 12 ∠ 0°
2nd Phasor: 20 ∠ 38.659808254090090604005862335173°
I used standard trig to derive the right-triangles run/rise:
Phasor 1 (X/Y): 12.0/0.0
Phasor 2 (X/Y): 15.6174/12.4939
Final Vector: 30.3119948A ∠ 24.34165138°
Final current: (30.3119948A * 1.732) = 52.5003749936A
Obviously, there are rounding errors, but this is as close as I could get to the purported Test answer. My $0.02..... Any glaring mistakes with what I've done?