Answer
$C=111{}^\circ,b\approx 7.3$ and $c\approx 16.1$.
Work Step by Step
First we will find the value of C
Properties of a triangle:
Sum of three angle is $A+B+C=180{}^\circ $
$\begin{align}
& A+B+C=180{}^\circ \\
& 44{}^\circ +25{}^\circ +C=180{}^\circ \\
& C=180{}^\circ -69{}^\circ \\
& C=111{}^\circ
\end{align}$
Now, we will find the remaining sides using the ratio
$\frac{a}{\sin A}$, or $\frac{12}{\sin 44{}^\circ }$,
Now, we will use the law of sines to find b.
$\begin{align}
& \frac{b}{\sin B}=\frac{a}{\sin A} \\
& \frac{b}{\sin 25{}^\circ }=\frac{12}{\sin 44{}^\circ } \\
& b=\frac{12\sin 25{}^\circ }{\sin 44{}^\circ } \\
& b\approx 7.3
\end{align}$
Using the law of Sines again, we will find c.
$\begin{align}
& \frac{c}{\sin C}=\frac{a}{\sin A} \\
& \frac{c}{\sin 111{}^\circ }=\frac{12}{\sin 44{}^\circ } \\
& c=\frac{12\sin 111{}^\circ }{\sin 44{}^\circ } \\
& c\approx 16.1
\end{align}$
