Bearings — if a line has whole circle bearing (WCB) 120°, what is its reduced (quadrantal) bearing?
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AS 20° E
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BS 60° E
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CN 120° E
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DN 60° E
Answer
Correct Answer: S 60° E
Explanation
Introduction / Context:Reduced bearings express directions within one of four quadrants relative to north or south. Converting accurately from whole circle bearings (0°–360° clockwise from north) to reduced bearings is a routine but crucial task in plotting and computations.
Given Data / Assumptions:
- WCB = 120°.
- WCB is measured from north, clockwise.
- Reduced bearing should be stated as N/S θ E/W.
Concept / Approach:Angles 90°–180° lie in the southeast (SE) quadrant. The reduced bearing equals S (180° − WCB) E. Here, 180° − 120° = 60°, so the reduced bearing is S 60° E.
Step-by-Step Solution:
Identify the quadrant: 120° is between 90° and 180° → SE.Compute interior angle with south: 180° − 120° = 60°.State reduced bearing: S 60° E.Verification / Alternative check:Sketching the axes confirms the direction: 30° beyond east towards south does not fit; it is indeed 60° east of south.
Why Other Options Are Wrong:
- S 20° E: Wrong magnitude.
- N 120° E / N 60° E: These lie in NE quadrant, not SE.
Common Pitfalls:Confusing which reference (north or south) to use per quadrant; 90°–180° always references south.
Final Answer:S 60° E