Mathematics, Coordinate Geometry, and Adjustments
What this domain tests
Traverse computations, coordinate geometry, area, curves, closures, and adjustments. Expect you to compute a misclosure and apply a correction correctly.
Core rules
- Latitude = distance × cos(bearing), departure = distance × sin(bearing). North and east are positive.
- Closure = sum of latitudes and departures. Linear misclosure = √(ΔN² + ΔE²); relative precision = perimeter / misclosure.
- Compass (Bowditch) rule distributes corrections in proportion to leg length: correction = −misclosure × (leg length / perimeter).
- Area by coordinates: A = ½ |Σ(XᵢYᵢ₊₁ − Xᵢ₊₁Yᵢ)|.
- For circular curves, keep the degree-of-curve definition consistent (arc vs chord).
Worked example
A traverse has misclosure ΔN = +0.30 ft, ΔE = −0.40 ft, perimeter 1,000 ft. Linear misclosure = 0.50 ft; relative precision = 1:2,000. For a 250-ft leg, compass-rule corrections are −0.30 × 250/1,000 = −0.075 ft in latitude and +0.40 × 250/1,000 = +0.100 ft in departure. Apply the correction before computing final coordinates.
Traps
Applying corrections with the wrong sign; adjusting angles but not distances; using the wrong curve definition; and reporting more precision than the evidence supports.