Answer
$A=80{}^\circ,a\approx 39.5$ and $c\approx 10.4$.
Work Step by Step
First we will find the value of A
Properties of the triangle:
Sum of three angles is $A+B+C=180{}^\circ $
$\begin{align}
& A+B+C=180{}^\circ \\
& A+85{}^\circ +15{}^\circ =180{}^\circ \\
& A=180{}^\circ -100{}^\circ \\
& A=80{}^\circ
\end{align}$
Now, we will find the remaining sides using the ratio
$\frac{b}{\sin B}$,or $\frac{40}{\sin 85{}^\circ }$,
Now, we will use the law of sines to find a.
$\begin{align}
& \frac{a}{\sin A}=\frac{b}{\sin B} \\
& \frac{a}{\sin 80{}^\circ }=\frac{40}{\sin 85{}^\circ } \\
& a=\frac{40\sin 80{}^\circ }{\sin 85{}^\circ } \\
& a\approx 39.5
\end{align}$
Using the law of sines again, we will find c.
$\begin{align}
& \frac{c}{\sin C}=\frac{b}{\sin B} \\
& \frac{c}{\sin 15{}^\circ }=\frac{40}{\sin 85{}^\circ } \\
& c=\frac{40\sin 15{}^\circ }{\sin 85{}^\circ } \\
& c\approx 10.4
\end{align}$
