<|system|>
What is the value of $x$ in the diagram?

[asy]
import olympiad;
draw((0,0)--(sqrt(3),0)--(0,sqrt(3))--cycle);
draw((0,0)--(-3,0)--(0,sqrt(3))--cycle);
label("8",(-3/2,sqrt(3)/2),NW);
label("$x$",(sqrt(3)/2,sqrt(3)/2),NE);
draw("$45^{\circ}$",(1.5,0),NW);
draw("$30^{\circ}$",(-2.45,0),NE);
draw(rightanglemark((0,sqrt(3)),(0,0),(sqrt(3),0),5));
[/asy]</s>.
<|user|>
Can you answer based on context?
<|assistant|>
First, we label the diagram:

[asy]
import olympiad;
draw((0,0)--(sqrt(3),0)--(0,sqrt(3))--cycle);
draw((0,0)--(-3,0)--(0,sqrt(3))--cycle);
label("8",(-3/2,sqrt(3)/2),NW);
label("$x$",(sqrt(3)/2,sqrt(3)/2),NE);
draw("$45^{\circ}$",(1.4,0),NW);
draw("$30^{\circ}$",(-2.4,0),NE);
draw(rightanglemark((0,sqrt(3)),(0,0),(sqrt(3),0),5));
label("$A$",(0,0),S);
label("$B$",(-3,0),W);
label("$C$",(sqrt(3),0),E);
label("$D$",(0,sqrt(3)),N);
[/asy]

Triangle $ABD$ is a 30-60-90 triangle, so $AD = BD/2 = 4$.

Triangle $ACD$ is a 45-45-90 triangle, so $CD = AD \sqrt{2} = 4\sqrt{2}$.