- 2075 Chaitra · 6 marks
Mean direction, two sets, stations A and B
Short answer
Using mean direction method, set I angle=121°00′25″, set II=121°00′35″; mean horizontal angle AOB = 121°00′30″.
Using mean direction method, calculate the mean horizontal angle.
| Instrument at | Sighted to | Set | HCR Left Face | HCR Right Face |
|---|---|---|---|---|
| O | A | I | 00°00′00″ | 179°59′30″ |
| B | I | 121°00′00″ | 301°00′20″ | |
| A | II | 90°00′10″ | 269°59′40″ | |
| B | II | 211°00′40″ | 31°00′20″ |
Method. In each set the mean direction of each target is found from the two faces, mean direction = [Face L + (Face R - 180°)]/2. The angle AOB in the set is the difference of the mean directions of B and A. The mean of the two sets is the final angle.
| Set | Sighted to | Face L | Face R | Face R - 180° | Mean direction | Angle AOB |
|---|---|---|---|---|---|---|
| I | A | 00°00′00″ | 179°59′30″ | 359°59′30″ | 359°59′45″ | |
| B | 121°00′00″ | 301°00′20″ | 121°00′20″ | 121°00′10″ | 121°00′25″ | |
| II | A | 90°00′10″ | 269°59′40″ | 89°59′40″ | 89°59′55″ | |
| B | 211°00′40″ | 31°00′20″ | 211°00′20″ | 211°00′30″ | 121°00′35″ |
(Face R - 180° for A in set I is 359°59′30″, i.e. -0°00′30″, and the mean of 0°00′00″ and -0°00′30″ is -0°00′15″ = 359°59′45″. For B in set II, 31°00′20″ + 180° = 211°00′20″.)
The two sets differ by 0°00′10″, which is small, so the result is accepted.
Answer: mean horizontal angle AOB = 121°00′30″.
✓ Answer checked by Claude Opus 5.5 (high effort)
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