KS3 Maths Bearings Explained With Clear Diagrams
A bearing describes a direction as an angle measured clockwise from north. KS3 questions use maps, scale diagrams and journeys to test careful interpretation of direction. Most mistakes begin before any calculation: students start from east, measure anticlockwise, or omit the leading zero from a three-figure answer. Clear diagrams and consistent steps make the subject much more manageable.
What is a three-figure bearing?
Bearings are measured clockwise from the north line at the starting point and are written using three digits. Due east is 090°, due south is 180°, due west is 270°, and north is 000° or 360° depending on the question’s convention. A direction 40° clockwise from north is written 040°, not 40° when a three-figure bearing is requested. Place a north arrow at the correct starting point before measuring anything.
Measure clockwise from north
Imagine standing at point A and looking towards B. Draw a vertical north line through A, then turn clockwise until your direction matches the line from A to B. The angle through which you turn is the bearing of B from A. Do not measure from the horizontal line just because it looks easier. If the direction points south-east, the result should lie between 090° and 180°. This rough estimate is an excellent check.
Find the reverse bearing
If the bearing of B from A is 065°, the bearing of A from B is 245°, found by adding 180°. If the original bearing exceeds 180°, subtract 180° instead. For example, the reverse of 290° is 110°. Draw north arrows at both points and show the journey in opposite directions to understand why the angles differ by half a full turn. The method assumes both bearings use parallel north reference lines.
Draw a bearing using a protractor
First mark the starting point and draw a north arrow. Align the protractor correctly with north, measure the stated clockwise angle, mark it and draw a ray through that mark. If the instruction says 135°, the direction should point south-east. A common mistake is using the wrong scale on a dual-scale protractor. Before drawing a long distance line, check the quadrant of the expected direction.
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Combine bearings with distances
A map might ask a student to travel 5 km on a bearing of 090° and then another 4 km on a bearing of 180°. The final position is 5 km east and 4 km south of the starting point. Draw a right-angled route and use Pythagoras where appropriate to determine the straight-line distance, √(5² + 4²) = √41 km. Do not confuse the bearing of the second leg with the bearing from the original start to the endpoint.
A dependable bearings checklist
Circle the words 'from' and 'to', locate the correct starting point, add north at that location and measure clockwise. Check that the angle has three figures and matches the approximate compass direction. Use separate north arrows at different points when finding reverse bearings. For a complex geometry question, identify the basic bearing facts before introducing triangle angle rules or trigonometry.
Frequently asked questions
Are bearings always clockwise?
Yes, standard three-figure bearings are measured clockwise from north.
Why do bearings use three digits?
This convention helps distinguish bearings such as 005° and 050° clearly.
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