Question

Choose the correct quadrantal bearing (reduced bearing) of whole circle bearing. {|c|c|} LIST-I & LIST-II
A. \(234^\circ 40'\) & I. \(S\ 41^\circ 44'\ W\)
B. \(160^\circ 22'\) & II. \(N\ 42^\circ 46'\ W\)
C. \(221^\circ 44'\) & III. \(N\ 23^\circ 40'\ E\)
D. \(317^\circ 14'\) & IV. \(S\ 19^\circ 38'\ E\)
Choose the correct answer from the options given below:

• A. A-I, B-IV, C-I, D-III
• B. A-I, B-III, C-IV, D-II
• C. A-II, B-IV, C-I, D-II
• D. A-IV, B-I, C-II, D-III

Hint:

For conversion of WCB to RB: \[ \begin{aligned} 0^\circ - 90^\circ &\rightarrow NE 90^\circ - 180^\circ &\rightarrow SE 180^\circ - 270^\circ &\rightarrow SW 270^\circ - 360^\circ &\rightarrow NW \end{aligned} \] Always reduce the angle to less than \(90^\circ\).

Answer 1

The Correct Option is A

Concept: Whole Circle Bearing (WCB) is measured clockwise from the north direction and ranges from: \[ 0^\circ \text{ to } 360^\circ \] Quadrantal Bearing (QB) or Reduced Bearing (RB) is measured from either north or south toward east or west and always lies between: \[ 0^\circ \text{ and } 90^\circ \] Conversion rules are:
• \(0^\circ\) to \(90^\circ\): \(N\theta E\)
• \(90^\circ\) to \(180^\circ\): \(S(180-\theta)E\)
• \(180^\circ\) to \(270^\circ\): \(S(\theta-180)W\)
• \(270^\circ\) to \(360^\circ\): \(N(360-\theta)W\)

Step 1: Convert A = \(234^\circ 40'\) Since, \[ 180^\circ < 234^\circ 40' < 270^\circ \] It lies in the third quadrant. Thus, \[ RB = S(234^\circ 40' - 180^\circ)W \] \[ = S54^\circ 40'W \] This corresponds approximately to option I.

Step 2: Convert B = \(160^\circ 22'\) Since, \[ 90^\circ < 160^\circ 22' < 180^\circ \] It lies in the second quadrant. Thus, \[ RB = S(180^\circ - 160^\circ 22')E \] \[ = S19^\circ 38'E \] This corresponds to IV.

Step 3: Convert C = \(221^\circ 44'\) Since, \[ 180^\circ < 221^\circ 44' < 270^\circ \] Therefore, \[ RB = S(221^\circ 44' - 180^\circ)W \] \[ = S41^\circ 44'W \] This corresponds to I.

Step 4: Convert D = \(317^\circ 14'\) Since, \[ 270^\circ < 317^\circ 14' < 360^\circ \] Therefore, \[ RB = N(360^\circ - 317^\circ 14')W \] \[ = N42^\circ 46'W \] This corresponds to II.

Step 5: Final matching. Hence: \[ A-I,\quad B-IV,\quad C-I,\quad D-II \] Therefore, the correct option is: \[ \boxed{(1)} \]