Bearings for IGCSE Maths
Three-figure bearings and solving bearing problems using trigonometry. This subtopic is part of Trigonometry in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understand
What You Need to Know
Three-figure bearings and solving bearing problems using trigonometry. This subtopic is part of Trigonometry in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding bearings is essential for achieving a strong grade in your IGCSE Maths exam.
Understanding Bearings
Bearings are three-figure angles measured clockwise from North. They are always written with three digits (e.g. 045°, not 45°). IGCSE 0580 tests bearings in both Core and Extended: drawing diagrams, calculating bearings using angle properties of parallel lines, and combining with trigonometry to find distances. The reverse bearing (from B to A given the bearing from A to B) is a standard exam question — add or subtract 180°.
Step-by-Step Method
- 1
Draw a clear diagram
Always draw the North arrow at each point. Mark all given angles and distances. This earns marks and prevents errors.
- 2
Mark the bearing correctly
Measure clockwise from North. Bearings are always three digits: 005°, 045°, 135°, 270°. Never write 90° — write 090°.
- 3
Use angle properties
North lines are parallel, so use alternate angles (Z), corresponding angles (F), or co-interior angles (C) to find angles inside the triangle formed by the bearings.
- 4
Apply trigonometry or Cosine/Sine Rule
Once you have the triangle with known sides and/or angles, apply SOH CAH TOA (right-angled) or Sine/Cosine Rule (non-right-angled) to find the unknown.
- 5
Find the reverse bearing
If the bearing from A to B is less than 180°, the bearing from B to A = bearing + 180°. If bearing from A to B is ≥ 180°, subtract 180°.
Worked Example
Question
Point B is 12 km from point A on a bearing of 070°. Point C is 8 km from A on a bearing of 130°. Find the distance BC, correct to 3 significant figures.
Solution
Step 1: Draw North from A. Mark AB = 12 km at 070° and AC = 8 km at 130° from North. Step 2: The angle BAC = 130° − 70° = 60°. Step 3: Use the Cosine Rule (two sides and included angle). BC² = AB² + AC² − 2 × AB × AC × cos(60°) BC² = 12² + 8² − 2 × 12 × 8 × 0.5 BC² = 144 + 64 − 96 BC² = 112 Step 4: BC = √112 = 10.583... ≈ 10.6 km Answer: BC = 10.6 km (3 s.f.)
Exam Tips for Bearings
- Always draw a clear, labelled diagram — bearing questions without a diagram nearly always lead to wrong angles.
- Three-figure bearings: 005° not 5°, 090° not 90°. Missing the leading zero costs a mark.
- North lines are always vertical and parallel — use this to extract angles inside the triangle using Z, F, and C angle rules.
- The reverse bearing trick: if bearing A→B is x°, then bearing B→A is (x + 180°) if x < 180°, or (x − 180°) if x ≥ 180°.
Practice Questions
Q1: A ship sails from port P on a bearing of 125° for 30 km to reach point Q. Write down the bearing of P from Q.
Show hint
The bearing from Q back to P = 125° − 180° = −55°? No — add 180°: 125° + 180° = 305°.
Q2: From a lighthouse L, ship A is on a bearing of 050° at a distance of 15 km. Ship B is due East of L at a distance of 20 km. Find the bearing of ship B from ship A.
Show hint
Draw North at L and at A. Find the angle at A between North and AB using the triangle LAB and parallel North lines.
Q3: Two hikers start at the same point. Hiker 1 walks 8 km on a bearing of 040°. Hiker 2 walks 6 km on a bearing of 310°. Find the distance between them.
Show hint
The angle between their directions = 360° − 310° + 40° = 90°. Use Pythagoras.
Frequently Asked Questions
What is bearings in IGCSE Maths?
Three-figure bearings and solving bearing problems using trigonometry.
Is bearings in the Core or Extended syllabus?
Bearings is part of the Core and Extended syllabus for IGCSE Mathematics 0580.
How do I revise bearings effectively?
Start with the revision notes to understand key concepts, then work through the worked examples step by step. Finally, practise past paper questions under timed conditions. Teacher Rig recommends spending focused revision sessions on bearings rather than trying to cover everything at once.
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