Answer
The required solution is $\text{698}\ \text{miles}$
Work Step by Step
The radius of the earth $ r $ is $4000\ \text{miles}$.
The angle $\theta $ at the center between A and B is $10{}^\circ $.
So, convert $\theta $ into radians:
$\begin{align}
& \theta =10{}^\circ \left( \frac{\pi }{180{}^\circ } \right) \\
& =\frac{\pi }{18}
\end{align}$
And the distance $ s $ between A and B is given by
$ s=r\theta $
Put $4000\ \text{miles}$ for $ r $ and $\frac{\pi }{18}$ for $\theta $:
$\begin{align}
& s=\left( 4000\ \text{miles} \right)\left( \frac{\pi }{18} \right) \\
& =\frac{2000\pi }{9}\ \text{miles}
\end{align}$
Put $\pi =3.14159$:
$\begin{align}
& s=\frac{2000\left( 3.14159 \right)}{9}\ \text{miles} \\
& \text{=698}\text{.13}\approx \text{698}\ \text{miles}
\end{align}$
