Answer
$B =105^\circ$
$b \approx4.72$,
$c \approx1.67$
Work Step by Step
1. Find the third angle $B=180-55-20=105^\circ$
2. Use the Law of Sines $\frac{4}{sin55^\circ}=\frac{b}{sin105^\circ}=\frac{c}{sin20^\circ}$
3. $b=\frac{4sin105^\circ}{sin55^\circ}\approx4.72$,
$c=\frac{4sin20^\circ}{sin55^\circ}\approx1.67$
