Standard deviation of the geodetic quadrilateral point coordinates determined by the application of Hansen's method

The Danish astronomer Peter Andreas Hansen, who also worked on theoretical geodesy, provided an original solution for solving the geodetic quadrilateral in which the four angles and the length of one side are known. This procedure, identified in scientific literature as Hansen's problem, has been applied in geodesy but significantly more so when solving various problems related to mining measurements in underground exploitation. Nonetheless, the literature does not cover the determining of the standard deviation of the coordinates of unknown points which are established using Hansen's method. In this paper then, equations are derived to calculate the standard deviation of the coordinates determined by the above mentioned procedure.