We know $\angle A=45^\circ, \angle B=15^\circ,$ and $BC=\sqrt{6}.$ What is AB

We know $\angle A=45^\circ, \angle B=15^\circ,$ and $BC=\sqrt{6}.$ What is AB

 

[asy]
size(5cm);
pair A,B,C;
A=(0,0);
B=(5,0);
C=(1,1);

draw(A--B--C--A);

label("$A$",A,SW);
label("$B$",B,SE);
label("$C$",C,N);

[/asy]