Magnetic Declination 10° W – Correct Corrections for Bearings (Whole-Circle and Quadrantal) If the local magnetic declination is 10° W (magnetic north is 10° west of true north), which statements about converting magnetic bearings to true bearings are correct?

Introduction / Context:
Magnetic declination links magnetic bearings (MB) to true bearings (TB). Correctly applying the sign convention is crucial, especially when working with reduced (quadrantal) bearings where the reference is N or S and the angle is measured toward E or W. Here declination is 10° W, meaning magnetic north lies west of true north.

Given Data / Assumptions:

• Declination = 10° W.
• Whole-circle bearing (WCB) is measured clockwise from north (0°–360°).
• Quadrantal (reduced) bearing (RB) is measured from N or S toward E or W by the acute angle.

Concept / Approach:

The standard conversion for whole-circle bearings is TB = MB + declination, taking east positive and west negative. Thus with 10° W: TB = MB − 10°. For reduced bearings, one must consider how the RB is derived from the azimuth: different quadrants flip the reference between north and south, which changes the sign of the correction in alternating quadrants.

Step-by-Step Solution:

Verification / Alternative check:

Test with a sample MB = 80° (NE): TB = 70° (lower), confirming negative correction in NE. For MB = 260° (SW): TB = 250°; SW reduced bearing decreases by 10°, consistent with the derived signs.

Why Other Options Are Wrong:

(b) and (c) assert wrong signs; (d) cannot hold because only (a) is correct; choosing (a) alone would ignore the explicit quadrantal statements, making (e) the precise selection.

Common Pitfalls:

Forgetting the “east positive, west negative” convention; mixing up azimuth adjustments with reduced-bearing quadrant changes.

Final Answer:

Only the whole-circle rule is correct; the stated quadrantal signs are reversed