Question $7(9$ points$)$

A total station is set up over an occupied point, A$.$ The surveyor sights a known point $B,$ and turns an angle right of $164\mathrm{.}5472$ to point $C$ and measures the horizontal distance AC $.$ What are the coordinates $($northing$,$ easting$)$ of C $?$

Given: Coordinates of A: N $113\mathrm{.}28,$ E $300\mathrm{.}05$

Bearing of line BA: S $5342{42}^{\text{'}\text{'}}$ W$,$ Horizontal distance measured $($AC$)$: $321\mathrm{.}78$ ft $.$

$N=139\mathrm{.}39,E=100\mathrm{.}80$

$N=159\mathrm{.}39,E=150\mathrm{.}80$

$N=129\mathrm{.}39,E=120\mathrm{.}80$

$N=149\mathrm{.}39,E=140\mathrm{.}80$