$(10$ points$)$ Determine the size and the number of poles of a power circuit breaker to protect a $480\frac{Y}{277}V$ lighting panel for an office building. The total panel load is $350$ kW with a power factor of $0\mathrm{.}90.$ The instantaneous short$-$circuit current at the panel is estimated to be $47,000A.($data provided in appendix A$\mathrm{.}1)$