--- title: "Link traverse ABCDEF, last line 108°05′40″" subject: "Surveying I" chapter: 4 key: "semester_3/surveying_i:link-traverse-abcdef-108-05-40" source: https://www.bctengineer.com/q/semester_3/surveying_i/link-traverse-abcdef-108-05-40 site: BCT Engineering --- # Link traverse ABCDEF, last line 108°05′40″ Surveying I · Chapter 4: The Compass - Asked in: 2076 Chaitra, 6 marks; 2076 Asoj, 8 marks (asked 2 times) - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/link-traverse-abcdef-108-05-40 - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4 ## Question The fore bearing of line AB of a link traverse ABCDEF is 61°06′00″. The angles to the right at stations, observed with theodolite, are ∠B = 93°06′50″, ∠C = 155°45′30″, ∠D = 247°09′40″ and ∠E = 90°58′20″. If the bearing (BB) of the last line observed was 108°05′40″, check whether the observations for angles are correct or not. If not, compute the correct bearings of all lines. ## Short answer Computed bearings of lines BC–EF using FB_next = FB_prev + 180° + angle, reducing. Computed FB of EF is 288°06′20″; observed FB 288°05′40″ gives misclosure –40″. Permissible error 40″, so observations just acceptable. Correction per angle –10″. Corrected fore bearings: AB 61°06′00″, BC 334°12′40″, CD 309°58′00″, DE 17°07′30″, EF 288°05′40″. ## Answer In a link traverse the bearing of the last line, computed from the first bearing and the observed angles, must agree with its observed bearing. The difference is the angular misclosure. **Rule (angles to the right):** $\text{FB of next line} = \text{FB of previous line} + 180^\circ + \text{angle to the right}$ (subtract multiples of $360^\circ$ to bring the result between $0^\circ$ and $360^\circ$). #### Step 1: Bearings computed from the observed angles | Line | Working | Computed FB | |---|---|---| | AB | given | 61°06′00″ | | BC | 61°06′00″ + 180° + 93°06′50″ | 334°12′50″ | | CD | 334°12′50″ + 180° + 155°45′30″ − 360° | 309°58′20″ | | DE | 309°58′20″ + 180° + 247°09′40″ − 720° | 17°08′00″ | | EF | 17°08′00″ + 180° + 90°58′20″ | 288°06′20″ | #### Step 2: Angular misclosure The observed back bearing of EF is 108°05′40″, so its observed FB is 108°05′40″ + 180° = 288°05′40″. $$ \text{Misclosure} = \text{observed} - \text{computed} = 288^\circ 05'40'' - 288^\circ 06'20'' = -0^\circ 00'40'' $$ So the angles are **not exactly correct**: there is a misclosure of 40″. Assuming a theodolite with least count $C = 20''$, the permissible misclosure is $C\sqrt{n} = 20''\sqrt{4} = 40''$, so the error is just within the limit and the angles are adjusted equally. #### Step 3: Adjustment The total correction is −0°00′40″. It is distributed equally over the 4 observed angles: −0°00′40″ / 4 = −0°00′10″ per angle. The correction to each line is −0°00′10″ multiplied by the number of angles used to reach it. | Line | Computed FB | Correction | Corrected FB | Corrected BB | |---|---|---|---|---| | AB | 61°06′00″ | 0 | 61°06′00″ | 241°06′00″ | | BC | 334°12′50″ | −0°00′10″ | 334°12′40″ | 154°12′40″ | | CD | 309°58′20″ | −0°00′20″ | 309°58′00″ | 129°58′00″ | | DE | 17°08′00″ | −0°00′30″ | 17°07′30″ | 197°07′30″ | | EF | 288°06′20″ | −0°00′40″ | 288°05′40″ | 108°05′40″ | Check: the corrected FB of the last line equals the observed value, 288°05′40″. **Answer:** misclosure = −40″ (the observations are not exactly correct, but are within the 40″ permissible limit). Corrected FBs: AB 61°06′00″, BC 334°12′40″, CD 309°58′00″, DE 17°07′30″, EF 288°05′40″ (the BBs differ by 180°; see the table). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which rule gives the FB of the next line from angles to the right? A. FB next = FB previous + 180° + angle to the right (adjust by 360°) B. FB next = FB previous - 180° - angle C. FB next = FB previous + angle only D. FB next = BB previous - angle Answer: A. Add 180° and the right-hand angle, then add or subtract 360° to bring it within 0°-360°. (Key point: Bearing rule for right angles) 2. Given FB of EF = 288°05'40'' and computed FB = 288°06'20''. What is the misclosure (given - computed)? A. +40'' B. -40'' C. -20'' D. -4° Answer: B. 288°05'40'' - 288°06'20'' = -40''. (Key point: Angular misclosure) 3. With least count 20'' and n = 4 angles, what is the permissible misclosure? A. 80'' (20'' x 4) B. 20'' C. 40'' (20'' x sqrt(4)) D. 10'' Answer: C. Permissible = C x sqrt(n) = 20'' x 2 = 40'', so the 40'' error is just acceptable. (Key point: Permissible misclosure) 4. How is the total correction of -40'' applied to the bearings? A. -40'' to every line B. -10'' to the last line only C. -40'' to the first line only D. -10'' per angle, multiplied by the number of angles used to reach each line Answer: D. The correction is equally distributed (-10'' per angle) and accumulates along the traverse: BC -10'', CD -20'', DE -30'', EF -40''. (Key point: Distributing correction) ## Close variants set in other exams - [Link traverse ABCDEF, right turn angles](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-right-turn-angles-22-17) — Surveying I, chapter 4, asked 3× ## Related in Surveying I - [Link traverse XP to TY, angles to right](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-xp-ty-angles-to-right) — Surveying I, chapter 4 - [Theodolite traverse ABCDA with missing VCR (68°30′10″)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atheodolite-traverse-abcda-hcr-vcr-68-30-10) — Surveying I, chapter 7 - [Open traverse ABCDEFGH, deflection angles](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aopen-traverse-deflection-angles-81-45) — Surveying I, chapter 4, asked 2× - [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 - [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: 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 ## Related in other subjects - [Link traverse Q to X, Gale's table m1, m2](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alink-traverse-qx-gale-m1-m2) — Surveying II, chapter 1