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 3
For the Red River water storage yard, a materials reviewer preparing a resident-engineer calculation check converts a traverse leg of 440 ft at bearing angle 30 degrees east of north. What northing increment is produced?
- A224.01 ft
- B311.00 ft
- C352.30 ft
- D381.05 ft
Show the answer and worked solution
Answer: D — 381.05 ft
Worked solution
- Step 1. Use northing projection
Delta N = L cos theta
Delta N = 440 cos(30 deg) = 381.05 ft
Why the other choices are wrong
- Choice A
- This figure comes out noticeably above the true northing projection for the stated leg and bearing, and it cannot be traced to any single substitution such as dividing by cosine instead of multiplying, or reversing the sine and cosine terms. The correct northing increment is simply the leg length multiplied by cos(theta).
- Choice B
- This total lands well under the projection that Delta N = L cos(theta) produces for this bearing, and it doesn't correspond to dropping the cosine factor, substituting sine for cosine, or using the 90-degree complement of the given angle. Recompute the northing directly as L times cos(theta) using the stated leg length and bearing angle.
- Choice C
- This number is inflated well beyond what the projection formula returns for this traverse leg, and no ordinary slip - wrong trig function, wrong angle reference, or unit mix-up - reproduces it cleanly. Apply Delta N = L cos(theta) with the given length and bearing angle to obtain the true northing increment.