Problem $2(30$ points$).$ Table $1$ shows the uncorrected values of the latitude and departures of each side of a closed traverse. Calculate the following:

$($a$)$ The bearing of each side.

$($b$)$ The distance of each side.

Add columns to the table to show the calculated bearings and distances. Show all calculations clearly for each side.

Problem $3(30$ points$).$ Using the distances calculated in Problem $2,$ perform the following tasks:

$($a$)$ Calculate the closing error.

$($b$)$ Calculate the precision of the survey.

$($c$)$ Perform the compass$-$rule adjustments and calculate the corrected latitude and departure of each side. Add columns to the table to show the correction to latitude and departure, corrected latitude and corrected departure for each side. Show all calculations clearly for each side.

Table $1.$ Latitudes and departures of a closed traverse

$\backslash$table$[[$Side$,$Latitude $(ft),$Departure $(ft)$