Answer
See below.
Work Step by Step
$C=180-A-B=180-55-64=61^\circ$.
Using the law of sines, $\frac{a}{\sin55^\circ}=\frac{34}{\sin61^\circ}\\a=\frac{34\sin55^\circ}{\sin61^\circ}\approx31.84$
$\frac{b}{\sin64^\circ}=\frac{34}{\sin61^\circ}\\b=\frac{34\sin64^\circ}{\sin61^\circ}\approx34.94$
