Answer
$A=50{}^\circ,a\approx 1757.9$ and $c\approx 1879.7$.
Work Step by Step
First we will find the value of A.
Properties of a triangle:
The sum of three angles is $A+B+C=180{}^\circ $
$\begin{align}
& A+B+C=180{}^\circ \\
& A+5{}^\circ +125{}^\circ =180{}^\circ \\
& A=180{}^\circ -130{}^\circ \\
& A=50{}^\circ
\end{align}$
Now, we will find the remaining sides using the ratio
$\frac{b}{\sin B}$,or $\frac{200}{\sin 5{}^\circ }$,
Now, we will use the law of sines to find a.
$\begin{align}
& \frac{a}{\sin A}=\frac{b}{\sin B} \\
& \frac{a}{\sin 50{}^\circ }=\frac{200}{\sin 5{}^\circ } \\
& a=\frac{200\sin 50{}^\circ }{\sin 5{}^\circ } \\
& a\approx 1757.9
\end{align}$
Using the law of sines again, we will find c.
$\begin{align}
& \frac{c}{\sin C}=\frac{b}{\sin B} \\
& \frac{c}{\sin 125{}^\circ }=\frac{200}{\sin 5{}^\circ } \\
& c=\frac{200\sin 125{}^\circ }{\sin 5{}^\circ } \\
& c\approx 1879.7
\end{align}$
