12.1 Mixed Boundary and COGO Scenario

Scenario: deed call, occupation, and coordinate closure

A client requests a retracement of a small commercial parcel. The subject deed reads: from an iron pin at the POINT OF BEGINNING, N 45°00'00" E, 200.00 ft to a found 5/8" rebar; thence S 45°00'00" E, 150.00 ft; thence S 45°00'00" W, 200.00 ft; thence N 45°00'00" W back to the POB. The adjoining deed calls the second course at 148 ft, not 150 ft. A 60-year-old fence runs roughly 1.5 ft inside the computed east line. Your closed traverse ties to two NGS control points, and three original monuments are found.

This is a classic mixed FS item. The first question is never "which formula?" It is "what does the item ask, and what controls?" If the stem asks for a coordinate, coordinate geometry (COGO) controls. If it asks for the best line or the next professional step, boundary law and real property principles control. If it asks how to report the 2-ft discrepancy, business and documentation control. Decide the deliverable, then compute only what supports it.

Apply the priority (dignity) of calls

When record terms conflict, surveyors weigh evidence in a recognized order. The exam expects you to recognize, not blindly apply, this hierarchy.

The found 5/8" rebar (an artificial monument, rank 3) outranks the 150-ft vs 148-ft distance conflict (rank 6). So you hold the monument and let the distance adjust. The fence, at 1.5 ft, is occupation evidence — it may support unwritten-rights analysis, but on the FS it is weighed, not automatically controlling.

Working the coordinate geometry

Now compute. Lay the POB at N 5000.00, E 5000.00. For each course, latitude = distance × cos(bearing) and departure = distance × sin(bearing), with sign set by quadrant (NE: +lat, +dep; SE: −lat, +dep; SW: −lat, −dep; NW: +lat, −dep). For the first course, N 45° E, 200.00 ft:

• Latitude = 200.00 × cos 45° = +141.42 ft
• Departure = 200.00 × sin 45° = +141.42 ft
• Corner 2: N 5141.42, E 5141.42

Repeat for each leg. The closure check is the heart of the COGO portion: sum the latitudes and the departures around the loop. For a closed figure they should sum to zero. The linear misclosure equals √(ΣLat² + ΣDep²), and the closure ratio = perimeter ÷ misclosure (reported as 1:N). A ratio of 1:10,000 is far better than 1:2,500.

Disciplined checks before you answer

1. Sketch it. A 30-second box sketch catches quadrant and sign errors faster than re-reading options.
2. Confirm the deliverable. Distance, bearing, coordinate, area, or closure ratio? Options often differ only by which one.
3. Watch the calculator angle mode. Bearings are in degrees-minutes-seconds; the DMS key on an approved Casio fx-115/fx-991 or TI-30X/TI-36X prevents decimal-degree slips.
4. Preserve precision until the last step; round once.
5. Reasonableness: a 200-ft urban lot line should not invert to a 2,000-ft coordinate jump.

Do not let a clean coordinate answer override a boundary issue. If the item asks "what controls the east line," the answer is the found monument, even though your COGO produced a tidy number two feet away. Numbers and judgment work together, and on mixed items the surveying principle usually decides the final choice.

Inverse, area, and reporting the conflict

Many mixed items end with an inverse — given two coordinates, find the distance and bearing between them. The handbook gives both relations: distance = √(ΔN² + ΔE²) and azimuth from north = arctan(ΔE / ΔN), then resolve the quadrant from the signs of ΔN and ΔE. Here the negative-north, positive-east signs place it in the SE quadrant — a bearing of about S 45°00' E. A frequent trap is taking the raw arctangent without checking the quadrant from the coordinate differences, which can throw the bearing into the wrong half of the compass.

If the item asks for area, the coordinate (shoelace) method is the exam's workhorse: 2A = |Σ(Eᵢ(Nᵢ₊₁ − Nᵢ₋₁))|, then divide by two; an answer in square feet may need conversion to acres at 43,560 ft² per acre. Keep the corners in a consistent clockwise or counterclockwise order, or the sign flips.

Closing the boundary–business loop

The last move is professional, not arithmetic. The 2-ft record discrepancy and the fence offset are facts you must document, not bury. A defensible retracement shows the held monuments, the rejected calls, the measured values, and a written rationale tying the result to the priority of calls. The table below maps each scenario fact to the FS area it tests and the action that earns the point.

Practicing this end-to-end — read records, apply the dignity of calls, run the COGO with closure and inverse checks, compute area, then write one sentence on the boundary issue and one on the computation check — trains exactly the integrated judgment the FS rewards. The candidates who struggle are usually strong at one half (the math or the law) and weak at switching between them under time pressure.