Latitudes, Departures and Traverse Closure practice problems for the FE Civil exam

A traverse is reduced by turning each measured course into two components: a latitude, which is the north-south component, and a departure, which is the east-west component. Latitude is the course length times the cosine of its bearing angle, and departure is the length times the sine. That pairing is the single fact these questions test, and reversing it is the error the distractors are built around. Remember that the bearing angle is measured from the north-south meridian, which is why cosine goes with the north-south component. Signs carry the direction: a course bearing north has a positive latitude, south is negative, east is a positive departure, west negative. Once every course is reduced, the sums close the figure. For a closed traverse the latitudes should sum to zero and the departures should sum to zero; whatever is left over is the closure error in each direction, and the linear misclosure is the square root of the sum of their squares. Precision is expressed as that misclosure divided by the total traverse perimeter, reported as a ratio such as one in five thousand. On the exam the arithmetic is short, so the points ride on the sine-cosine pairing and the signs.

Key formulas

Latitude, the north-south component: latitude = L * cos(bearing)
Departure, the east-west component: departure = L * sin(bearing)
Closure error in each direction: e_lat = sum(latitudes); e_dep = sum(departures)
Linear misclosure: e = sqrt(e_lat^2 + e_dep^2)
Precision of the traverse: precision = e / perimeter, reported as 1:N

Common mistakes

Swapping sine and cosine, which puts the east-west component in the north-south column.
Dropping the sign, so that a south latitude and a north latitude add instead of cancelling.
Measuring the bearing from the east-west axis instead of from the meridian.
Reporting the closure error itself when the question asked for the precision ratio.

5 worked practice problems

Commit to an answer before opening the solution. Each problem shows the governing model, every substitution, a unit check, and why each wrong choice is wrong.

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Background reading

Original question written by FE Exam AI Prep from the public FE Civil exam specification. Before release, a solver model re-derived the answer twice from the question alone, without its answer key, and a critic model checked the result. No licensed engineer reviews these questions. It is not an NCEES question and does not come from any NCEES practice exam. FE Exam AI Prep is an independent study tool and is not affiliated with, endorsed by, or sponsored by NCEES.

Latitudes, Departures and Traverse Closure practice problems for the FE Civil exam

Key formulas

Latitude, the north-south component: latitude = L * cos(bearing)
Departure, the east-west component: departure = L * sin(bearing)
Closure error in each direction: e_lat = sum(latitudes); e_dep = sum(departures)
Linear misclosure: e = sqrt(e_lat^2 + e_dep^2)
Precision of the traverse: precision = e / perimeter, reported as 1:N

Common mistakes

Swapping sine and cosine, which puts the east-west component in the north-south column.
Dropping the sign, so that a south latitude and a north latitude add instead of cancelling.
Measuring the bearing from the east-west axis instead of from the meridian.
Reporting the closure error itself when the question asked for the precision ratio.

5 worked practice problems

Commit to an answer before opening the solution. Each problem shows the governing model, every substitution, a unit check, and why each wrong choice is wrong.