Answer
$a \approx15.88$
$B \approx57.5^\circ$
$C\approx 70.5^\circ$
Work Step by Step
1. Use the Law of Cosines, $a=\sqrt {(17)^2+(19)^2-2(17)(19)cos52^\circ}\approx15.88$
2. Use the Law of Sines $\frac{15.88}{sin52^\circ}=\frac{17}{sinB}=\frac{19}{sinC}$
3. Thus $B=sin^{-1}(\frac{17sin52^\circ}{15.88})\approx57.5^\circ$
4. Find the third angle $C\approx180-52-57.5=70.5^\circ$
