Question

The statements below show the relationship of Whole Circle Bearing (WCB) with the Quadrantal Bearing (QB) for quadrant designations North-East (N-E), North-West (N-W), South-East (S-E) and South-West (S-W). Which of the following statements is/are correct?

• A. For the quadrant S-W, QB = WCB −180°
• B. For the quadrant S-W, WCB = 180° − QB
• C. For the quadrant N-W, WCB = 180° − QB
• D. For the quadrant N-W, QB = − WCB + 360°

Hint:

To convert between WCB and QB, identify the quadrant first. In the S-W quadrant, use: ${QB} = {WCB} - 180^\circ$.

Answer 1

The Correct Option is A

Whole Circle Bearing (WCB) is measured clockwise from the north, ranging from \(0^\circ\) to \(360^\circ\).
Quadrantal Bearing (QB) is measured from the north or south towards the east or west, ranging from \(0^\circ\) to \(90^\circ\).

For the S-W quadrant:
WCB lies between \(180^\circ\) and \(270^\circ\).
QB is measured from the south towards the west.
The relation is: \[ \text{QB} = \text{WCB} - 180^\circ \] Thus, Option (A) is correct.

Other options are incorrect based on quadrant conversion rules:
(B): Incorrect; this reverses the formula for QB.
(C): Incorrect; in the N-W quadrant, WCB = \(360^\circ - \text{QB}\)
(D): Incorrect and syntactically ambiguous; it appears mathematically incorrect.