Answer
The missing values are: $A=43{}^\circ,a\approx 171.9\text{ and }b\approx 241.0$.
Work Step by Step
For any triangle,
The law of sines states:
$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\operatorname{sinC}}$
Then use the angle sum property and obtain:
$\begin{align}
& A+B+C=180{}^\circ \\
& A+107{}^\circ +30{}^\circ =180{}^\circ \\
& A=180{}^\circ -137{}^\circ \\
& A=43{}^\circ
\end{align}$
Using the law of sines we get,
$\begin{align}
& \frac{a}{\sin A}=\frac{c}{\operatorname{sinC}} \\
& \frac{a}{\sin 43{}^\circ }=\frac{126}{\sin 30{}^\circ } \\
& a\cdot \sin 30{}^\circ =126\cdot \sin 43{}^\circ \\
& a=\frac{126\cdot \sin 43{}^\circ }{\sin 30{}^\circ }
\end{align}$
This gives $a\approx 171.9$ to the nearest tenth.
Also,
$\begin{align}
& \frac{b}{\sin B}=\frac{c}{\sin C} \\
& \frac{b}{\sin 107{}^\circ }=\frac{126}{\sin 30{}^\circ } \\
& b\cdot \sin 30{}^\circ =126\cdot \sin 107{}^\circ \\
& b=\frac{126\cdot \sin 107{}^\circ }{\sin 30{}^\circ }
\end{align}$
This gives $b\approx 241.0$ to the nearest tenth.
So, $A=43{}^\circ,a\approx 171.9\text{ and }b\approx 241.0$.
