01 — Explanation
What are the three rules every bearing must follow?
- Measured from North — North is always the reference line.
- Measured clockwise — never anticlockwise.
- Three-figure notation — always written with exactly three digits, so becomes and becomes .
Exam Tip
Omitting the leading zero (writing instead of ) 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 apart:
Example: the bearing of A from B is . Since , the reverse (B from A) is .
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 , which is exactly where the 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 or segments.
04 — Explanation
How do I plot a point given a bearing and a scaled distance?
- Convert the real distance to a drawing distance using the scale (e.g. means ).
- Draw a North line at the start point.
- Centre your protractor on the start point, align with North, and measure the bearing clockwise.
- 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. ) — 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 () can finish the problem.
07 — Worked example
Worked example
The bearing of a lighthouse L from a harbour H is . 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?
- The known bearing is , which is less than .
- Reverse bearing .
- The bearing of H from L is .