Answer
$b \approx1.03$
$A \approx 160.3^\circ$
$C\approx 9.7^\circ$
Work Step by Step
1. Use the Law of Cosines, we have $b=\sqrt {(2)^2+(1)^2-2(2)(1)cos10^\circ}\approx1.03$
2. Use the Law of Sines, $\frac{sinA}{2}=\frac{sin10^\circ}{1.03}$, thus $A=sin^{-1}(\frac{2sin10^\circ}{1.03})\approx 19.7^\circ$ or $160.3^\circ$ (choose the second answer as side $a$ is the longest)
3. We have $C\approx(180-160.3-10)=9.7^\circ$
