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, and the arithmetic was re-run as an executable calculation. 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: FE Civil practice problem 1
For the Bayshore detention pond retrofit, a civil analyst preparing a field-change evaluation converts a traverse leg of 540 ft at bearing angle 55 degrees east of north. What northing increment is produced?
- A187.10 ft
- B233.65 ft
- C309.73 ft
- D269.81 ft
Show the answer and worked solution
Answer: C — 309.73 ft
Worked solution
- Step 1. Use northing projection
Delta N = L cos theta
Delta N = 540 cos(55 deg) = 309.73 ft
Why the other choices are wrong
- Choice A
- This result falls about 40% short of L*cos(theta) = 540*cos(55 deg) = 309.73 ft, well beyond what a degree or minute rounding slip in the bearing angle would cause; the northing increment equals the traverse leg length multiplied by the cosine of the bearing angle given.
- Choice B
- This northing component lands about 25% below L*cos(theta) = 540*cos(55 deg) = 309.73 ft, far more than a sine for cosine swap at this bearing angle would create; the correct increment comes from multiplying the traverse leg length by the cosine of the bearing angle measured from north.
- Choice D
- This value runs about 13% below L*cos(theta) = 540*cos(55 deg) = 309.73 ft, a gap too large for reading the bearing from the wrong reference line or rounding the angle to explain; the northing increment must come from the leg length times the cosine of the stated bearing angle only.