Bearing conversion: A line has magnetic bearing = 32° and magnetic declination = 10° 15′ W (west is negative). What is the true bearing (from true north, clockwise)?

Difficulty: Easy

Correct Answer: 21° 45′

Explanation:


Introduction / Context:
Converting magnetic bearings to true bearings is a frequent need when using compass observations together with maps referenced to true north. The key is handling magnetic declination with the correct sign convention: easterly declination adds, westerly declination subtracts.


Given Data / Assumptions:

  • Magnetic bearing (MB) = 32°.
  • Magnetic declination (west) = 10° 15′ (treated as negative).
  • True bearing (TB) is measured clockwise from true north, expressed as a single angle.


Concept / Approach:
For conversion: TB = MB + declination, with east positive and west negative. Since declination is westerly, subtract its magnitude. Therefore TB = 32° − 10° 15′ = 21° 45′. True bearings are typically given as a single clockwise angle without quadrant letters.


Step-by-Step Solution:

Write the relation: TB = MB + declination.Use sign convention: westerly = negative.Compute: 32° − 10° 15′ = 21° 45′.State the final TB: 21° 45′ (clockwise from true north).


Verification / Alternative check:
Graphically, rotate the magnetic meridian west of true north by 10° 15′; the true bearing must be smaller than the magnetic one by exactly that amount, confirming 21° 45′.


Why Other Options Are Wrong:

  • 42° 15′: Would imply an easterly (positive) declination.
  • 42° 15′ W / 21° 45′ W: True bearings are not typically annotated with E/W quadrantal tags in this format.


Common Pitfalls:
Mixing up signs; a quick rule is “East is least? No—East adds; West subtracts” when converting MB to TB.


Final Answer:
21° 45′

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