A surveyor has completed two different closed traverses. Traverse A was surveyed using a modern Total Station, where both angles and distances were measured with extremely high precision. Traverse B was surveyed using an older transit and a steel tape, where the angles were measured somewhat precisely, but the taped distances were considered much less reliable due to rough terrain and temperature fluctuations.

Recommend the most appropriate mathematical method for balancing (adjusting) each traverse and justify your choice based on the principles of each rule.

A surveyor runs a closed traverse around a large property boundary. After measuring all the interior angles and closing the shape, they find an angular misclosure of 2 minutes, which is well within acceptable limits for the project. However, after calculating the latitudes and departures, they discover a linear error of closure that is massive—over 5 meters off.

What is the most likely source of this error, and why does angular closure not guarantee linear accuracy?

A closed four-sided traverse ABCD has the following unadjusted data:

Calculate the latitude and departure for each line, then determine the Linear Error of Closure (LEC) and the Relative Error of Closure (REC).

A closed traverse has a total perimeter of $1000 \text{ m}$. The total error in latitude ($e_L$) is $+0.50 \text{ m}$ and the total error in departure ($e_D$) is $-0.30 \text{ m}$. Line AB is $250 \text{ m}$ long with an unadjusted latitude of $+180.00 \text{ m}$ and an unadjusted departure of $+173.20 \text{ m}$.

Calculate the corrections for Line AB using the Compass Rule and state its final adjusted latitude and departure.

Using the data from Problem 2 ($e_L = +0.50 \text{ m}$, $e_D = -0.30 \text{ m}$), assume the sum of the absolute values of all latitudes ($\Sigma |L|$) in the traverse is $800.00 \text{ m}$ and the sum of the absolute values of all departures ($\Sigma |D|$) is $750.00 \text{ m}$. Line AB has an unadjusted latitude of $+180.00 \text{ m}$ and an unadjusted departure of $+173.20 \text{ m}$.

Calculate the corrections for Line AB using the Transit Rule and state its final adjusted latitude and departure.