Question 479118
if B=30 degrees, C=45 degrees, then A=180-(B+C) degrees, 
A=180-(30+45)=105 degrees
Use  the law of sines 
{{{a/sina=c/sinc}}}
{{{(sqrt(3)+1)/sin105=c/sin45}}}multiply by {{{sin45}}}
{{{c=((sqrt(3)+1)sin45)/sin105}}}
{{{sin45=sqrt(2)/2}}}
{{{sin105=sin(180-75)=sin75=sin(30+45)=sin30*cos45+cos30*sin45=(1/2)*(sqrt(2)/2)+(sqrt(3)/2)*(sqrt(2)/2)=(sqrt(2)+sqrt(3)*sqrt(2))/4=(sqrt(2)(1+sqrt(3)))/4}}}
{{{c=((sqrt(3)+1)(sqrt(2)/2))/((sqrt(2)(1+sqrt(3)))/4)=(cross((sqrt(3)+1))*cross(sqrt(2))*4)/(cross(sqrt(2))*cross((1+sqrt(3)))*2)=4/2=2}}}
Answer {{{c=2}}}