Answer
$\angle A=100^{\circ}$
$a=89.4$
and
$c=70.5$
Work Step by Step
I. Need to find the last angle.
$\angle A+29^{\circ}+51^{\circ}=180^{\circ}$
$\implies \angle A=100^{\circ}$
II. Use law of sines formula to find $a$ and $c$
$\dfrac{\sin 100^{\circ}}{a}=\dfrac{\sin 29^{\circ} }{44}=\dfrac{\sin 51^{\circ} }{c}$
This implies that
$a=\dfrac{44 \sin 100^{\circ} }{\sin 29^{\circ}}=89.4$
and
$c=\dfrac{44 \sin 51^{\circ} }{\sin 29^{\circ}}=70.5$
