--- title: "Corrected and true bearings, 8°40′E" subject: "Surveying I" chapter: 4 key: "semester_3/surveying_i:true-bearings-declination-8-40e" source: https://www.bctengineer.com/q/semester_3/surveying_i/true-bearings-declination-8-40e site: BCT Engineering --- # Corrected and true bearings, 8°40′E Surveying I · Chapter 4: The Compass - Asked in: 2062 Baisakh, 10 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/true-bearings-declination-8-40e - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4 ## Question The following bearings were observed in running a compass traverse. | Line | Fore bearing | Back bearing | |---|---|---| | AB | 66°15′ | 244°0′ | | BC | 129°45′ | 313°0′ | | CD | 218°30′ | 37°30′ | | DA | 306°45′ | 126°45′ | Find the corrected fore and back bearings, and the true bearings of the lines, given that the magnetic declination is 8°40′E. ## Short answer Corrected fore bearings: AB 66°15', BC 132°00', CD 217°30', DA 306°45'. True bearings (magnetic +8°40'): AB 74°55', BC 140°40', CD 226°10', DA 315°25'. ## Answer Line DA has FB − BB = 180°00′, so stations D and A are free; B and C are suspected. Declination is 8°40′ East, so **true bearing = magnetic bearing + 8°40′**. Local attraction at a station is detected by comparing the fore bearing (FB) and back bearing (BB) of each line: if there is no local attraction at either end, $\text{FB} - \text{BB} = 180^\circ$ exactly. #### Step 1: Check each line | Line | FB | BB | FB − BB | Remark | |---|---|---|---|---| | AB | 66°15′ | 244°00′ | 182°15′ | Differs by +2°15′ | | BC | 129°45′ | 313°00′ | 176°45′ | Differs by −3°15′ | | CD | 218°30′ | 37°30′ | 181°00′ | Differs by +1°00′ | | DA | 306°45′ | 126°45′ | 180°00′ | Free, difference = 180° | Line DA has a difference of exactly 180°, so stations D and A are free from local attraction. The other stations are corrected one after another, starting from A. #### Step 2: Correct the stations in turn - Line AB: FB at A = 66°15′ is correct. The correct BB is 246°15′, observed 244°00′, so the correction at B is +2°15′. - Line BC: FB at B = 129°45′ with correction +2°15′ gives 132°00′. The correct BB is 312°00′, observed 313°00′, so the correction at C is −1°00′. - Line CD (check): FB at C = 218°30′ with correction −1°00′ gives 217°30′. The correct BB is 37°30′, which equals the observed value, so D needs no correction, as expected. | Station | A | B | C | D | |---|---|---|---|---| | Correction | 0 | +2°15′ | −1°00′ | 0 | Stations affected by local attraction: B, C. #### Step 3: Corrected bearings | Line | Observed FB | Correction | Corrected FB | Observed BB | Corrected BB | True FB | True BB | |---|---|---|---|---|---|---|---| | AB | 66°15′ | 0 | 66°15′ | 244°00′ | 246°15′ | 74°55′ | 254°55′ | | BC | 129°45′ | +2°15′ | 132°00′ | 313°00′ | 312°00′ | 140°40′ | 320°40′ | | CD | 218°30′ | −1°00′ | 217°30′ | 37°30′ | 37°30′ | 226°10′ | 46°10′ | | DA | 306°45′ | 0 | 306°45′ | 126°45′ | 126°45′ | 315°25′ | 135°25′ | Check: corrected FB − corrected BB = 180° for every line. **Answer:** Corrected bearings: AB = 66°15′ / 246°15′, BC = 132°00′ / 312°00′, CD = 217°30′ / 37°30′, DA = 306°45′ / 126°45′ (FB / BB). True bearings (FB): AB = 74°55′, BC = 140°40′, CD = 226°10′, DA = 315°25′. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. With magnetic declination of 8°40′ East, how is true bearing found? A. True = magnetic − 8°40′ B. True = magnetic + 8°40′ C. True = magnetic, only BB changes D. True = 360° − magnetic Answer: B. East declination means the needle points east of true north, so true = magnetic + 8°40′. (Key point: East declination) 2. Line AB: FB at A = 66°15′ is correct, observed BB = 244°00′. What is the correction at B? A. −2°15′ B. +2°15′ C. +3°15′ D. 0 Answer: B. The correct BB is 246°15′; observed is 244°00′, so the correction is +2°15′. (Key point: Correction at B) 3. After station B (+2°15′), the FB of BC is corrected to 132°00′. The observed BB of BC is 313°00′. What is the correction at C? A. +1°00′ B. −3°15′ C. −1°00′ D. +3°15′ Answer: C. The correct BB is 312°00′, observed 313°00′ is 1°00′ too large, so the correction is −1°00′. (Key point: Correction at C) 4. What is the true FB of AB (corrected FB 66°15′)? A. 57°35′ B. 74°55′ C. 75°55′ D. 66°15′ Answer: B. True = 66°15′ + 8°40′ = 74°55′. (Key point: True bearing) ## Related in Surveying I - [Local attraction: AB 69°30′ compass traverse](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ab-69-30-reordered) — Surveying I, chapter 4 - [Corrected and true bearings, 5°E declination](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-true-bearings-5-deg) — Surveying I, chapter 4 - [Local attraction, bearings AB 305°00′ (EA 45°)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ea-305-00) — Surveying I, chapter 4, asked 2× - [Local attraction and true bearings, 1°30′E](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Acompass-closed-traverse-declination-1-30-east) — Surveying I, chapter 4 - [Local attraction, S 40°30′ W traverse](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-quadrantal-s40-30w) — Surveying I, chapter 4 - [Corrected bearings and interior angles, PQRST](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Acorrected-bearings-quadrantal-pq-s37-30e) — Surveying I, chapter 4 ## Related in other subjects - [Bearings of BC and CD in traverse ABCDE](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-abcde-bearings-bc-cd) — Surveying II, chapter 1, asked 2× - [Traverse missing length CD, bearing EA](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-missing-cd-length-ea-bearing) — Surveying II, chapter 1 - [Closed traverse missing EA bearing, BC length](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcdea-missing-ea-bc) — Surveying II, chapter 1 - [Missing bearings of BC and DE in traverse](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-missing-bearings-bc-de) — Surveying II, chapter 1