Answer
$A= 70^\circ$
$a \approx 10.82$
$c \approx 11.34$
Work Step by Step
Step 1. Using the given conditions, we have $A=180-100-10=70^\circ$
Step 2. Using the Law of Sines, we have $\frac{a}{sin70^\circ}=\frac{c}{sin100^\circ}=\frac{2}{sin10^\circ}$
Step 3. Thus $a=\frac{2sin70^\circ}{sin10^\circ} \approx 10.82$ and $c=\frac{2sin100^\circ}{sin10^\circ}\approx 11.34$