$15\mathrm{.}40$ It has been determined by test that the synchronous reactance $\backslash ($ X$\_\{$s$\}\backslash )$ and armature resistance $\backslash ($ R$\_\{$a$\}\backslash )$ of a $2,300-$V$,500-$VA$,$ three$-$phase synchronous generator are $8\mathrm{.}0$ and $\backslash (0\mathrm{.}1\backslash$Omega $\backslash ),$ respectively. If the machine is operating at rated load and voltage at a power factor of $0\mathrm{.}867$ lagging, find the generated voltage per phase and the torque angle.