$3/$ The horizontal coordinates $N_P$ and $E_P$ of a new point $P$ were determined from the measured horizontal distance $d$ and the geodetic azimuth $.$

The geodetic azimuth is $=45{00}^{\text{'}}{00}^{\text{'}\text{'}}$ and its standard deviation is ${}_{}=+-5".$

The horizontal distance is $d=1200m$ and its standard deviation is ${}_d=+-10cm.$

The horizontal coordinates of a given point are set to zero, so that $N=E=0\mathrm{.}00m.$

Compute the horizontal coordinates $N{P}_P$ and $E{P}_P$ of a new point $P$ and their standard deviations.

The result is:

a$.N_P=848\mathrm{.}53+-0\mathrm{.}07m$ and $E_P=848\mathrm{.}53+-0\mathrm{.}07m$

b$.N_P=848\mathrm{.}53+-0\mathrm{.}06m$ and $E_P=848\mathrm{.}53+-0\mathrm{.}05m$

c$.N_P=848\mathrm{.}53+-0\mathrm{.}05m$ and $E_P=848\mathrm{.}53+-0\mathrm{.}05m$

d$.N_P=848\mathrm{.}53+-0\mathrm{.}04m$ and $E_P=848\mathrm{.}53+-0\mathrm{.}04m$