How do you solve the triangle given #A=55^circ, B=42^circ, c=3/4#?

Let the top angle be#color(white)(aaaaaaaa)## 55°=angle A#
Let the bottom left angle be#color(white)(aa)# #42°=angleB#
Let the bottom Right angle be#color(white)(a)# #83°=angleC#
Let the left side #color(white)(aaaaaaaaaa)## =AB(c)#
Let the bottom side#color(white)(aaaaaaaa)## =BC(a)#
Let the Right side#color(white)(aaaaaaaaaa)## =AC(b)#

#:.180°-(55°+42°)=83°angleC#

#:.(AC)/SinB=(AB)/SinC#

#:.(AC)/Sin42°=(AB)/Sin83°#

multiply L.H.S. and R.H.S. by# color(blue)(color(white)(a)## color(blue)(sin42°#

#:.color(blue)cancelsin(42°)^1/1 xx (AC)/cancel(sin42°)=(0.75)/Sin83° xx color(blue)(Sin42°)/1#

#:.AC=(0.75 xx 0.669130606)/(0.992546151)#

#:.AC=0.501847954/0.992546151#

#:.AC=0.505616745#

to the nearest 3 decimal places

#:.color(blue)(AC=0.506#

#:.(BC)/SinA=(AB)/SinC#

#:.(BC)/Sin42°=(AB)/Sin83°#

multiply L.H.S. and R.H.S. by# color(blue)(color(white)(a)## color(blue)(sin55°#

#:.color(blue)cancelsin(55°)^1/1 xx (BC)/cancel(sin55°)=(0.75)/Sin83° xx color(blue)(Sin55°)/1#

#:.BC=(0.75 xx 0.8191522044)/(0.992546151)#

#:.BC=0.614364033/0.992546151#

#:.BC=0.6189778#

to the nearest 3 decimal places

#:.color(blue)(BC=0.619#