If the Whole Circle Bearing of a line AB is 132° 35' 45'’ then the Whole Circle Bearing of line BA will be
- A47° 24' 15'’
- B222° 35' 45'’
- C227° 24' 15'’
- D312° 35' 45'’Correct
Solution
Concept
The bearing of line AB in the direction of measurement is called Fore Bearing (FB), and the bearing of the same line in the opposite direction (line BA) is called Back Bearing (BB).
Formula
Back Bearing = Fore Bearing ± 180° Use +180° if Fore Bearing < 180°, and -180° if Fore Bearing > 180°.
Step-by-step solution
1. Identify the given Fore Bearing (FB) of line AB: 132° 35' 45". 2. Check if the FB is less than or greater than 180°. Here, 132° 35' 45" is less than 180°. 3. Add 180° to find the Back Bearing (WCB of line BA): 132° 35' 45" + 180° = 312° 35' 45". Answer: (D) 312° 35' 45'’
Explanation
The line BA is exactly in the opposite direction of line AB. Because opposite directions differ by 180°, we add 180° to the bearing of AB since it is less than 180°.
Why the other options are wrong
A: This comes from subtracting 132° 35' 45" from 180° incorrectly. B: This comes from adding 90° instead of 180°. C: Incorrect arithmetic calculation.
Shortcut
If FB < 180°, just add 180° to get the BB.
Common mistake
Subtracting 180° instead of adding it, or subtracting from 360° incorrectly.
Correct answer: D) 312° 35' 45'’