This topic summary covers Knowledge Organiser: Bearings within Bearings for GCSE Mathematics. Revise Bearings in Geometry & Measures for GCSE Mathematics with 19 exam-style questions and 5 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 9 of 9 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Bearings
Key Terms
- Bearing: A direction expressed as a 3-digit angle measured clockwise from North
- Back bearing: The bearing to return to the starting point
- North line: The vertical reference line drawn at the measurement point
- Transversal: A line crossing two parallel North lines (use alternate angles)
Must-Know Facts
- Three rules: 3 digits, from North, clockwise — always
- N = 000°, E = 090°, S = 180°, W = 270°
- Back bearing: if bearing < 180° → add 180°; if > 180° → subtract 180°
- Draw a North line at EVERY point you measure from
- Combine with SOHCAHTOA or Pythagoras for distance problems
Key Methods
- Back bearing = original bearing ± 180°
- North/South component = distance × cos(angle from N/S)
- East/West component = distance × sin(angle from N/S)
- Total distance = √(N/S² + E/W²) using Pythagoras
Key Formulas
- Bearings are measured clockwise from North, always 3 digits (e.g. 045°)
- Back bearing = bearing + 180° (if ≤ 180°) or bearing − 180° (if > 180°)
- North/South component = distance × cos(bearing angle)
- East/West component = distance × sin(bearing angle)
Common Mistakes
- Not measuring from North: Bearings are always measured clockwise from North — not from East or from the previous direction
- Forgetting 3 digits: Write 045° not 45° — bearings always have 3 digits
- Back bearing direction: Add or subtract 180° depending on whether the bearing is above or below 180°
- Scale drawings: Use a protractor carefully and measure from the correct North line at each point
Practice questions for Bearings
A ship travels in the direction of North-East. Which of the following correctly writes this as a three-figure bearing?
Explain how to find the back bearing (return bearing) of any given bearing. Your answer should cover both cases.
Quick recall flashcards
Bearing of East
090° (quarter turn clockwise from North)
Bearing of West
270° (three-quarters turn clockwise from North)