Answer
(a) $30\mathrm{km}$
(b) $60\mathrm{km}$
(c)$20^o$
Work Step by Step
(a) Distance from the epicenter to A:
\begin{align*}
EA=&AB\tan 30^o\\
=&50\times {1\over\sqrt{3}}\\
=&50\times 1.732\\
EA=&30\mathrm{km}
\end{align*}
(b) Distance from the epicenter to B:
\begin{align*}
EB=&{AB\over \cos 30^o}\\
=&{50\over 0.866}\\
EB=&60\mathrm{km}
\end{align*}
(c) Direction of epicenter from C:
\begin{align*}
\tan\theta=&{EA\over AC}\\
=&{30\over 50+20}\\
=&0.4\\
\theta=&\tan^{-1}(0.4)\\
\theta=&20^o\\
\end{align*}
