Bearing conversion — special direction: If the whole circle bearing (WCB) of a line is 270°, what is its reduced (quadrantal) bearing expressed in the standard N/S θ E/W format?

Introduction / Context:Whole circle bearings (0°–360° clockwise from north) and reduced (quadrantal) bearings (N/S θ E/W with θ ≤ 90°) are two common ways to express directions. Converting correctly avoids plotting errors and miscommunication between field notes and computations.

Given Data / Assumptions:

• WCB = 270°.
• Reduced bearing uses a north or south reference with an acute angle to east or west.
• Angles are measured in degrees.

Concept / Approach:A WCB of 270° points exactly west. In reduced bearing notation, due west can be written as S 90° W or N 90° W; both are equivalent in direction because 90° west of north or south is the same line. To avoid ambiguity in multiple-choice settings, we pick one conventional form, typically S 90° W, and explicitly note it is due west.

Step-by-Step Solution:

Verification / Alternative check:Sketch the axes: north at 0°, east at 90°, south at 180°, west at 270°. The line at 270° is unmistakably west, matching S 90° W.

Why Other Options Are Wrong:

• N 90° E: Due east, not west.
• S 45° W and N 60° W: Southwest and northwest directions, not exactly west.

Common Pitfalls:Writing “90° W” or “W 90°” which are not standard reduced-bearing formats; using N 90° W interchangeably in tests that require a single unique option.

Final Answer:S 90° W (due west)