Bearings look like one of the simpler ideas in geometry: measure from north, turn clockwise, write three digits. Then a question arrives with a map, two labelled points and a lot of blank space, and marks vanish for reasons that feel mysterious. In practice, nearly every lost mark in a bearings question comes from one of five familiar slips. Knowing what they are, and what to do instead, is most of the work.
1. Measuring anticlockwise, or from the wrong line
A bearing is an angle measured clockwise from a north line, and it is always measured at the point you are standing on. Both halves of that sentence cause trouble. Measure anticlockwise from north, or measure from the line pointing at the object instead of the line pointing north, and you will still produce a number that looks like a bearing — just not the right one.
Take a simple case. B lies to the north-east of A, at 40° to the right of the north line. Measuring anticlockwise gives 320°. The bearing of B from A is 040°.
The fix is to draw north before anything else. Sketch a short vertical line with an arrow at the point named after the word “from”. Then trace a clockwise arc from the north line to the line joining the two points, and mark that arc on the diagram. Estimate the quadrant first: north-east sits between 000° and 090°, south-east between 090° and 180°, south-west between 180° and 270°, north-west between 270° and 360°. If your answer lands in a different quadrant from your estimate, re-measure before writing anything down.
2. Writing two figures instead of three
047° is safe, but 47° looks like a bearing and is not one. Bearings are written with three figures so they can never be confused with an ordinary angle or a plain direction reading. That means 5° becomes 005°, 90° becomes 090°, and 47° becomes 047°. Due north is normally written 000°; some exam boards also accept 360°, so check which your teacher prefers.
The padding is not fussiness. Once you are adding and subtracting 180° to find reverse directions, three-figure form keeps the arithmetic honest: 047° plus 180° is 227°, and nobody has to guess whether a bare “47” meant a bearing or an interior angle.
3. Reusing the same bearing in the opposite direction
The reverse direction, sometimes called the back bearing, is the one that catches people most often. If the bearing of B from A is 047°, the bearing of A from B is not 047°. Stand at B, draw a north line there, and look back along BA: the angle is 227°.
The rule is short. Add 180° if the original bearing is 180° or less; subtract 180° if it is greater. From 047° you get 227°. From 310° you get 130°. The two north lines are parallel, and the angles they make with the same line AB are co-interior, which is why the difference is always 180°.
Two habits keep this reliable. Write the rule down before you use it, and check the sketch afterwards: a back bearing should point roughly opposite the original, so 227° for a line running north-east is plausible, while 227° for a line running north-west is not.
4. Forgetting the north line at each new point
Journey problems — A to B, then B to C — need a north line at every point, not just the first one. Students often draw one careful north line at A, then measure the turn at B relative to that line, or relative to AB, and wonder why the answer is out.
Draw a fresh north line at each stage, parallel to the first, and label it N. Parallel lines are the whole tool kit here: alternate and corresponding angles let you transfer a bearing from one point to another without measuring twice.
The related slip is mixing bearings with interior angles. In a triangle question, the angle inside the triangle at each vertex is not the bearing; you normally find the interior angles first and convert them afterwards, adding to or subtracting from the north direction. Keep the two quantities labelled separately in your working and do not blend them in one line of arithmetic.
5. Sloppy protractor work
Geometry marks are lost on technique as often as on understanding. The usual problems:
- The centre mark sits beside the point rather than on it. Place it exactly on the vertex and press down.
- The line is too short to reach the protractor’s edge. Extend it lightly in pencil, well past where the measuring arc will end.
- The 0° line is not aligned with the north line. Line them up, then check the north line reads 0 on the scale before reading anything else.
- The wrong scale is read. Protractors have two, running in opposite directions; use the one that starts at 0 on your north line.
- The answer is rounded carelessly or given with decimals. Unless told otherwise, give bearings to the nearest degree.
A final estimate takes five seconds and catches most of these. Before measuring, say the direction to yourself: north-east, between 000° and 090°. If the protractor gives you 280°, you know something has gone wrong — and roughly where.
A routine that catches all five
Every bearings question, whether it is a single measurement or a four-stage journey, can be handled the same way.
- Identify the point you are measuring from — the one named after “from” — and mark
Photo: 24278850 / Pixabay