Q.6 The following observations were made in an open-traverse compass survey. Bearing of Line AB is S 35° 30' E, whereas the included angles measured clockwise at stations B, C, D and E are 105° 20', 265° 50', 20° 10' and 325° 40', respectively. The bearing of Line CD is
- AS 24° 20' ECorrect
- BS 65° 40' W
- CS 24° 20' W
- DS 65° 40' E
Solution
Concept
With clockwise included angles, the bearing of the next line = bearing of the previous line + included angle ± 180°.
Formula
θnext = θprev + α ± 180° (subtract 360° if the result is more than 360°)
Step-by-step solution
1. Bearing of AB = S 35°30' E. As WCB: 180° - 35°30' = 144°30'. 2. Bearing of BC = 144°30' + 105°20' - 180° = 69°50'. 3. Bearing of CD = 69°50' + 265°50' - 180° = 155°40'. 4. 155°40' is in the SE quadrant. RB = 180° - 155°40' = 24°20'. 5. Bearing of CD = S 24°20' E. Answer is (A).
Explanation
First change the bearing of AB to whole circle bearing. Then add each clockwise included angle and subtract 180° to get the next line's bearing. The bearing of CD comes to 155°40', which is S 24°20' E.
Why the other options are wrong
B: S 65°40' W comes from wrong quadrant conversion. C: S 24°20' W has the right angle but the wrong quadrant, since 155°40' is in the SE quadrant. D: S 65°40' E uses the complement of the correct reduced bearing.
Shortcut
Next WCB = previous WCB + clockwise angle - 180°. Do this for each station, then convert to RB at the end.
Common mistake
Forgetting to convert the RB of AB to WCB first, or giving the wrong quadrant letter when converting back to RB.
Correct answer: A) S 24° 20' E