Answer
1.46
Work Step by Step
We first calculate the third angle $ C=\pi-A-B=\pi-\frac{\pi}{4}-\frac{\pi}{3}=\frac{5\pi}{12}$
Next we use the law of sines $\frac{a}{sinA}=\frac{c}{sinC}$, which leads to
$ a=\frac{c\cdot sinA}{sinC}=\frac{2sin\pi/4}{sin5\pi/12}=1.46$
