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Geometry & Measures · Foundation & Higher

Bearings

Bearings are a way of expressing direction using angles measured clockwise from North. They are always written as three digits (e.g. 045°, 270°).

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Key facts to remember

  • 1Bearings are measured clockwise from North.
  • 2Always written as three digits: e.g. 050°, not 50°.
  • 3North = 000°, East = 090°, South = 180°, West = 270°.
  • 4Back bearing (return journey) = bearing + 180° (if < 360°) or bearing − 180° (if ≥ 180°).
  • 5Use sine/cosine rules or scale drawings to find distances and angles.
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Worked examples

Example 1

A ship sails on a bearing of 065° for 40 km. Find the bearing for the return journey.

Working

  1. Return bearing = 065° + 180° = 245°
Answer245°
Example 2

Point B is on a bearing of 130° from A. Find the bearing of A from B.

Working

  1. The bearing of A from B is the back bearing
  2. 130° + 180° = 310°
Answer310°
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Common mistakes

✗Writing bearings with fewer than three digits (e.g. 45° instead of 045°).
✗Measuring angles anticlockwise instead of clockwise from North.
✗Forgetting that the bearing of A from B is different from the bearing of B from A.
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Exam tips

✓Always draw a North line at the point you are measuring from before marking the angle.
✓Remember: three digits, clockwise from North — double-check every bearing you write.

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