Answer
$a \approx5.23$
$B \approx46.0^\circ$
$C\approx 64.0^\circ$
Work Step by Step
1. Use the Law of Cosines, $a=\sqrt {(5)^2+(4)^2-2(5)(4)cos70^\circ}\approx5.23$
2. Use the Law of Sines $\frac{5.23}{sin70^\circ}=\frac{4}{sinB}=\frac{5}{sinC}$
3. Thus $B=sin^{-1}(\frac{4sin70^\circ}{5.23})\approx46.0^\circ$
4. Find the third angle $C\approx180-70-46.0=64.0^\circ$
