The bearings of two inaccessible stations, $S_1$ (Easting $500$ m, Northing $500$ m) and $S_2$ (Easting $600$ m, Northing $450$ m) from a station $S_3$ were observed as $225^{\circ}$ and $153^{\circ}\: 26’$ respectively. The independent Easting (in m) of station $S_3$ is:

1. $450.000$
2. $570.710$
3. $550.000$
4. $650.000$