过点A做AD垂直BC于点D,设CD=x
∵∠C=45,∠B=30,则AD=CD=x,AB=2,BD=√3x
∵a+c=1
∴3x+√3x=1
x=(3-√3)/6
b=√2×(3-√3)/6
=(3√2-√6)/6