Answer
$C =95^\circ$
$a \approx2.84$
$b \approx2.58$
Work Step by Step
Step 1. Using the given figure and conditions, we have $C=180-40-45=95^\circ$
Step 2. Using the Law of Sines, we have $\frac{a}{sin45^\circ}=\frac{b}{sin40^\circ}=\frac{4}{sin95^\circ}$
Step 3. Thus $a=\frac{4sin45^\circ}{sin95^\circ}\approx2.84$ and $b=\frac{4sin40^\circ}{sin95^\circ}\approx2.58$
