Bearings – Convert a Whole Circle Bearing to a Reduced (Quadrantal) Bearing A line has a whole circle bearing (WCB) of 290°. What is its reduced bearing (RB) expressed in quadrant notation?

Introduction:
Bearings can be given as whole circle bearings (0°–360° from true or magnetic north, clockwise) or reduced bearings (quadrantal form referenced to the nearest north or south toward east or west). Converting between forms is routine in traverse computation.

Given Data / Assumptions:

• WCB = 290°.
• RB format: N/S θ E/W depending on the quadrant.
• Angles measured from the north or south reference toward east or west.

Concept / Approach:

Locate the quadrant: 270°–360° corresponds to the northwest (NW) quadrant. The reduced bearing is the acute angle from the north toward the west for this quadrant: RB = N (360° − 290°) W = N 70° W.

Step-by-Step Solution:

Verification / Alternative check:

Alternative: from west reference, RB could be W 20° N, which is equivalent; however, standard RB convention prefers N/S first, so N 70° W is selected.

Why Other Options Are Wrong:

N 20° E is NE quadrant; N 20° W is too close to north; S 70° E and S 20° W are southern quadrants.

Common Pitfalls:

Subtracting from 180° instead of 360°; mixing RB letter order (N/S should be first).

Final Answer:

N 70° W