Question $3[40$ points$]$

A five$-$sided field traverse has the following balanced angles: A $=101\backslash$deg $2826$; B $=102\backslash$deg $1042$; C $=104\backslash$deg $4206$; D $=113\backslash$deg $0442$; E $=118\backslash$deg $3404.$ The lengths of the sides are as follows: AB $=50\mathrm{.}276$ m; BC

$=26\mathrm{.}947$ m; CD $=37\mathrm{.}090$ m; DE $=35\mathrm{.}292$ m; EA $=20\mathrm{.}845$ m$.$ The bearing of EA is N $20\backslash$deg $2020$ W$,$ and AB

is oriented northeasterly.

$1.$ Perform a check for angular closure.

$2.$ Compute the bearings for all sides.

$3.$ Compute the latitudes and departures.

$4.$ Compute the linear error of closure and the precision ratio.

$5.$ Using the data above and the compass rule, balance the latitudes and departures.

$6.$ Using the data above, compute the coordinates of stations C$,$ D$,$ E$,$ and B$.$ Assume that the

coordinates of station A are $1,000\mathrm{.}000$ m N and $1,000\mathrm{.}000$ m E$.$

$7.$ Use the coordinate method to compute the area of the enclosed figure.