A bearing is always measured from North, in a clockwise direction, and written as a 3-digit number (e.g. 045°, not 45°). The most common source of error isn't the trigonometry — it's drawing the diagram itself. Always draw a fresh North line at every point mentioned in the question, and measure your angle clockwise from that line, not from the line connecting the two points.
Bearings rarely test new trigonometry — most questions just recycle the sine rule, cosine rule, Pythagoras' theorem, and basic angle facts you already know. What actually loses marks is the diagram. Get the diagram wrong, and every angle you calculate afterwards is wrong too, even if your trigonometry is flawless.
The three rules below are non-negotiable and appear in the mark scheme every single time:
Measured from
North (000°)
Direction
Clockwise only
Format
3-digit number
This is the single biggest cause of mistakes. The bearing of B from A is measured using a North line drawn at A — not at B, and not along the line AB itself.
Correct — North line drawn at A, angle measured clockwise from North to AB
"The bearing of B from A" means: stand at A, face North, then rotate clockwise until you're facing B. The North line belongs at A. Students often draw the North line at the wrong point simply because they read the sentence too quickly.
The exact wording trap
"Bearing of B from A" ≠ "Bearing of A from B". These give completely different angles (they differ by 180°, since the two North lines point the same way but you're facing opposite directions). Always underline the word immediately after "from" in the question — that's where your North line goes.
A bearing of 45° must be written as 045°. A bearing of 8° must be written as 008°. This is a strict formatting rule in the O-Level mark scheme — writing "45°" instead of "045°" can cost a mark even if the angle itself is correct.
Key fact: all North lines are parallel to each other. North always points the same real-world direction, no matter which point on your diagram you draw it from. This is what lets you use angle facts for parallel lines — alternate angles, interior angles — to relate a bearing measured at one point to a bearing measured at another.
Town Q is on a bearing of 065° from Town P. Find the bearing of Town P from Town Q.
Bearing of Q from P = 065°. Bearing of P from Q = 065° + 180° = 245°
Solution
Quick rule for back bearings: if the original bearing is less than 180°, add 180°. If the original bearing is 180° or more, subtract 180°. This shortcut works because you're always looking back along the same line, just from the opposite end.
Ship A sails from port O on a bearing of 060° for 40 km to reach point A. Ship B sails from port O on a bearing of 140° for 55 km to reach point B. Find the distance AB.
Angle AOB = 140° − 060° = 80°. Now a standard SAS cosine rule setup.
Solution
140° − 060° = 80°.AB² = OA² + OB² − 2(OA)(OB)cos(AOB)AB² = 40² + 55² − 2(40)(55)cos80°AB² = 1600 + 3025 − 4400(0.1736)AB² = 4625 − 764.0 = 3861AB = √3861 = 62.1 km (3 s.f.)Common mistake
Students often use 140° or 060° directly as the triangle's included angle, instead of subtracting to find the actual angle AOB between the two lines. Always find the angle between the two lines first — bearings are directions from North, not the angle of the triangle itself.
These four are useful sanity checks. If your calculated bearing comes out negative, or greater than 360°, or doesn't roughly match the direction shown in your diagram, you've made an error — go back and check your subtraction or addition step. The same North-line habit carries over to angle of elevation and depression questions, where the reference line is horizontal instead of North.
Do I need a protractor to answer bearings questions in the exam?
No — O-Level bearings questions are solved using trigonometry (sine rule, cosine rule, angle facts), not by measuring with a protractor. Your diagram should be a reasonably accurate sketch to help you visualise the problem, but exact angles come from calculation, not measurement.
What's the difference between a bearing and a normal angle?
A normal angle can be measured from any reference line, in either direction, and is often written as a 1 or 2 digit number. A bearing is always measured from North specifically, always clockwise, and always written as exactly 3 digits (with leading zeros if needed, e.g. 007°).
How do I find a bearing greater than 180°?
Use the same method — draw North at the correct point, then measure clockwise. If the direction you need is, say, roughly West-North-West, your clockwise angle from North will naturally come out above 270°. Trust the clockwise rotation rather than trying to guess the size of the angle from the picture.
Why do parallel North lines matter for these questions?
Because North always points the same real-world direction, every North line you draw on your diagram — no matter which point it's drawn at — is parallel to every other North line. This lets you apply angle facts for parallel lines (alternate angles, interior angles) to relate the bearing at one point to the bearing at another, which is exactly how back bearings are derived.
— Mr Gan Math Tuition
Mr. Gan works with students who want a reliable diagram-first method — not guesswork under exam pressure.
Chat with Mr. Gan