Answer
$ \angle A=70^{\circ}$
$a=109.7$
and
$b=20.3$
Work Step by Step
I. Need to find the last angle.
$\angle A+10^{\circ}+100^{\circ}=180^{\circ}$
$\implies \angle A=70^{\circ}$
II. Use law of sines formula to find $a$ and $b$
$\dfrac{\sin 70^{\circ}}{a}=\dfrac{\sin 10^{\circ} }{b}=\dfrac{\sin 100^{\circ} }{115}$
This implies that
$a=\dfrac{115 \sin 70^{\circ} }{\sin 100^{\circ}}=109.7$
and
$b=\dfrac{115 \sin 10^{\circ} }{\sin 100^{\circ}}=20.3$
