Closed traverse data: AB — FB = 10°20', BB = 190°20'; BC — FB = 155°30', BB = 336°30'; CA — FB = 290°00', BB = 112°00'. The total error is:
Correct Answer: D. +3°00'
📚 Detailed Explanation: Closed Traverse Bearing Error = +3°00'
Why D (+3°00') is correct: The closed traverse has three lines. By checking fore and back bearings, local attraction at each station is identified and corrected. Tracking corrections propagates the error accumulation to the closing station, giving a total error of +3°.
Step-by-Step Local Attraction Analysis
| Line | Fore Bearing (FB) | Back Bearing (BB) | BB − FB | Difference from 180° |
|---|---|---|---|---|
| AB | 10°20' | 190°20' | 180°00' | 0 → A and B free of local attraction |
| BC | 155°30' | 336°30' | 181°00' | +1°00' at C |
| CA | 290°00' | 112°00' | −178°00' (= 182°) | Combined error |
Step 1: AB: BB – FB = 190°20′ – 10°20′ = 180°00′
→ No local attraction at A or B; all AB bearings are correct.
→ No local attraction at A or B; all AB bearings are correct.
Step 2: FB of BC = 155°30′ (correct since B is free)
True BB of BC = 155°30′ + 180°00′ = 335°30′
Observed BB of BC = 336°30′
Error at C = +1°00′ (station C has local attraction of +1°)
Step 3: Correct FB of CA:
Observed FB of CA = 290°00′
Corrected FB of CA = 290°00′ – 1°00′ = 289°00′ (subtract C’s error)
Step 4: True BB of CA should be:
True BB = 289°00′ – 180°00′ = 109°00′
Observed BB of CA at A = 112°00′
But A is free of local attraction (confirmed in Step 1)
Discrepancy = Observed – True = 112°00′ – 109°00′ = +3°00′
Total closing error = +3°00′
- Station A and B are free of local attraction (BB − FB = 180° exactly for line AB).
- Station C has local attraction error of +1°00'.
- After correcting for C's error, the closure check at A gives a total error of +3°00'.