- 2067 Asar · 9 marks
Link traverse XP to TY, angles to right
Short answer
Angular misclosure is +0°45′. Adjusted bearings: XP 148°15′, PQ 60°54′, QR 109°33′, RS 44°57′, ST 277°51′, TY 36°45′.
The following angles to the right were obtained in a closed link traverse between two adjusted known lines XP and TY. Compute the angular misclosure, if any, on that traverse and the adjusted bearings of the traverse lines.
| Station | Angle to the right | Bearing |
|---|---|---|
| X | ||
| P | 92°30′ | 148°15′ |
| Q | 228°30′ | |
| R | 115°15′ | |
| S | 52°45′ | |
| T | 298°45′ | |
| Y | 36°45′ |
Reading of the table: 148°15′ is the adjusted bearing of the known line XP and 36°45′ is the adjusted bearing of the known line TY. Angles are measured to the right at P, Q, R, S, T, so the bearing of the next line = bearing of the previous line + 180° + angle.
Rule (angles to the right): (add or subtract to bring the result between and ).
Step 1: Bearings computed from the observed angles
| Line | Working | Computed FB |
|---|---|---|
| XP | given | 148°15′ |
| PQ | 148°15′ + 180° + 92°30′ − 360° | 60°45′ |
| QR | 60°45′ + 180° + 228°30′ − 360° | 109°15′ |
| RS | 109°15′ + 180° + 115°15′ − 360° | 44°30′ |
| ST | 44°30′ + 180° + 52°45′ | 277°15′ |
| TY | 277°15′ + 180° + 298°45′ − 720° | 36°00′ |
Computed FB of TY = 36°00′; given (observed) FB of TY = 36°45′.
Step 2: Angular misclosure
The computed bearing of TY is 36°00′ against the known 36°45′: angular misclosure = +0°45′ (the computed bearing is 45′ less than the known one). It is distributed equally among the 5 angles (+9′ each).
Step 3: Adjustment
Total correction = +0°45′ (added to the computed bearing of the last line). It is distributed equally over the 5 observed angles: +0°45′ / 5 = +0°09′ per angle. The correction to a line is +0°09′ multiplied by the number of angles used to reach it.
| Line | Computed FB | Correction | Corrected FB | Corrected BB |
|---|---|---|---|---|
| XP | 148°15′ | 0 | 148°15′ | 328°15′ |
| PQ | 60°45′ | +0°09′ | 60°54′ | 240°54′ |
| QR | 109°15′ | +0°18′ | 109°33′ | 289°33′ |
| RS | 44°30′ | +0°27′ | 44°57′ | 224°57′ |
| ST | 277°15′ | +0°36′ | 277°51′ | 97°51′ |
| TY | 36°00′ | +0°45′ | 36°45′ | 216°45′ |
Check: corrected FB of the last line equals the observed value 36°45′.
Answer: angular misclosure = +0°45′. Adjusted bearings: XP 148°15′, PQ 60°54′, QR 109°33′, RS 44°57′, ST 277°51′, TY 36°45′.
✓ Answer checked by Claude Opus 5.5 (high effort)
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