Bearings

El método, paso a paso

1. 1

   Draw the north line at the starting point

   north line at A, then the line from A to B

   The bearing is always measured from the north line at the point you are travelling from. Drawing it first, before measuring anything, prevents the commonest error of measuring from the wrong end of the journey.

2. 2

   Measure clockwise from north

   north → east is 90° clockwise → bearing 090°

   Always clockwise, always from north, never anticlockwise and never from another direction. There are no exceptions to this, which makes bearings one of the more mechanical topics once the convention is secure.

3. 3

   Write three figures, always

   45° → 045° · 9° → 009°

   The leading zeros are required. A bearing written as 45 rather than 045 loses the mark even though the angle is right, and this accounts for a large share of the marks dropped in the topic.

4. 4

   Find a back bearing by adding or subtracting 180

   bearing of B from A is 070° → bearing of A from B is 250°

   Add 180 if the original is under 180, subtract 180 if it is over. The result must always land between 000 and 360, and that constraint decides which operation to use.

5. 5

   Use angle rules to work between bearings

   parallel north lines → alternate and co-interior angles apply

   North lines at different points are parallel, so the parallel-line angle rules connect bearings taken at different places. This is what turns a bearings question into an angle-chasing question, which is usually the intended route.

Three rules, no exceptions

Clockwise, from north, three figures. Every bearings question is an application of those three rules, and almost every lost mark is a breach of one of them. There is unusually little to understand here and unusually much to be precise about.

The three-figure rule exists because bearings are read aloud in navigation and aviation, where '045' is unambiguous and 'forty-five' could be misheard. Knowing why the convention exists helps students take it seriously rather than treating the zeros as optional.

• Measured clockwise
• Always from north
• Always three figures — 045°, not 45°
• Back bearing: ±180°, keeping the result under 360
• North lines are parallel — angle rules apply

'From' matters more than it looks

The bearing of B from A and the bearing of A from B are different numbers, differing by 180 degrees. Questions state which they want and students frequently measure from the wrong end, producing an answer that is exactly the back bearing of the correct one.

The habit that prevents it is to underline the word after 'from' before drawing anything, then put the north line at that point. It is a reading skill rather than a mathematical one, and it is where most of the difficulty actually lies.

Bearings with trigonometry

Higher-tier questions combine bearings with the sine and cosine rules, giving distances and directions between three points and asking for a missing one. The bearing work sets up the triangle and the trigonometry solves it.

The reliable approach is to draw the diagram, mark every north line, fill in every angle the parallel rules give you, and only then look for the triangle. Attempting the trigonometry before the diagram is complete is where these questions usually go wrong.

How we teach bearings

We mark the three-figure convention strictly from the first exercise. It seems harsh for an answer that is otherwise correct, and it is exactly how the exam will mark it, so learning it early costs nothing and learning it late costs marks.

We also teach students to draw the north line at every relevant point, not just the first. Bearings questions become angle-chasing questions once those parallel lines are on the page, and most students who are stuck simply have not drawn them.