- 2059 Chaitra · 10 marks
Mean angles BAC, CAD, DAE at A
Short answer
Compute mean direction = (FL + FR – 180°)/2. Mean directions: B=0°10′15″, C=62°10′20″, D=135°20′25″, E=250°30′30″. Subtract successive values: BAC=62°00′05″, CAD=73°10′05″, DAE=115°10′05″.
Find the mean horizontal angles BAC, CAD and DAE in the following cases.
| Instrument Stn | Target Stn | F.L. | F.R. |
|---|---|---|---|
| A | B | 0°10′10″ | 180°10′20″ |
| C | 62°10′10″ | 242°10′30″ | |
| D | 135°20′15″ | 315°20′35″ | |
| E | 250°30′20″ | 70°30′40″ |
Method. The instrument is at A and four targets B, C, D and E are observed on both faces. Mean direction of each target = [F.L. + (F.R. - 180°)]/2. The angle between two targets = difference of their mean directions.
| Inst. stn | Target | F.L. | F.R. | F.R. ∓ 180° | Mean direction |
|---|---|---|---|---|---|
| A | B | 0°10′10″ | 180°10′20″ | 0°10′20″ | 0°10′15″ |
| A | C | 62°10′10″ | 242°10′30″ | 62°10′30″ | 62°10′20″ |
| A | D | 135°20′15″ | 315°20′35″ | 135°20′35″ | 135°20′25″ |
| A | E | 250°30′20″ | 70°30′40″ | 250°30′40″ | 250°30′30″ |
(Check: BAE = 250°20′15″ = 62°00′05″ + 73°10′05″ + 115°10′05″.)
Answer: BAC = 62°00′05″, CAD = 73°10′05″, DAE = 115°10′05″.
✓ Answer checked by Claude Opus 5.5 (high effort)
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