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Pearson Edexcel 4MA1 IGCSE  ·  Topic G4.16

G4.16 Bearings

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01 — Explanation

What are the three rules every bearing must follow?

  1. Measured from North — North is always the 000°000° reference line.
  2. Measured clockwise — never anticlockwise.
  3. Three-figure notation — always written with exactly three digits, so 5°5° becomes 005°005° and 59°59° becomes 059°059°.

Exam Tip

Omitting the leading zero (writing 35°35° instead of 035°035°) loses a dedicated accuracy mark even when your angle calculation is entirely correct — treat the three-digit format as a non-negotiable final check.

02 — Explanation

How do I find the reverse bearing (the bearing back the other way)?

Because the North lines at two different points are parallel, the bearing of B from A and the bearing of A from B are always exactly 180°180° apart:

If known bearing<180°:reverse=known+180°\text{If known bearing} < 180°: \quad \text{reverse} = \text{known} + 180°
If known bearing≥180°:reverse=known−180°\text{If known bearing} \ge 180°: \quad \text{reverse} = \text{known} - 180°

Example: the bearing of A from B is 310°310°. Since 310≥180310\ge180, the reverse (B from A) is 310−180=130°310-180=130°.

03 — Explanation

Why does the \pm180° rule actually work geometrically?

The two parallel North lines mean the connecting path AB acts as a transversal. The angle at one end and the equivalent angle at the other are linked by alternate and co-interior angle facts — specifically, co-interior angles sum to 180°180°, which is exactly where the ±180°\pm180° shortcut comes from. If a question doesn't fit the simple rule neatly (e.g. it mixes quadrants), fall back on explicitly finding the interior angle via co-interior or alternate angles, then build up the full bearing from there using 90°90° or 180°180° segments.

04 — Explanation

How do I plot a point given a bearing and a scaled distance?

  1. Convert the real distance to a drawing distance using the scale (e.g. 1 cm:20 m1\text{ cm}:20\text{ m} means 140 m÷20=7 cm140\text{ m}\div20=7\text{ cm}).
  2. Draw a North line at the start point.
  3. Centre your protractor on the start point, align 0°0° with North, and measure the bearing clockwise.
  4. Measure the drawing distance along that line with a ruler and mark the point clearly with a cross.

Exam Tip

Always show the scale-conversion division explicitly (e.g. 140÷20=7140\div20=7) — omitting this working can cost a method mark even with a correctly plotted point.

05 — Explanation

How do I read a bearing or distance back off a completed scale drawing?

Draw a new North line at whichever point you're measuring from — don't reuse the North line drawn at a different point. Measure the angle clockwise from that new North line, and convert any measured drawing distance back to a real distance by multiplying by the scale factor.

06 — Explanation

How do I solve a multi-leg bearing problem (A to B to C)?

Draw a fresh North line at every turning point. To find the angle at B between the paths BA and BC, you typically need the reverse bearing of A from B first (using the rule above), then combine it with the given bearing of C from B — often via subtraction — to get the interior angle of the triangle ABC at that vertex. From there, the angle sum of a triangle (180°180°) can finish the problem.

07 — Worked example

Worked example

The bearing of a lighthouse L from a harbour H is 148°148°. A boat sails from H on this bearing for 6 km to reach L, then turns and sails back to H. What is the bearing of H from L?

  1. The known bearing is 148°148°, which is less than 180°180°.
  2. Reverse bearing =148+180=328°= 148+180=328°.
  3. The bearing of H from L is 328°328°.