Sheet № 61 · Foundation + Higher · AQA · Edexcel · OCR
Bearings –
Bearings is a practical geometry topic that appears on both Foundation and Higher tier GCSE Maths papers for AQA, Edexcel, and OCR. A bearing is a way of describing direction using angles measured clockwise from north. You need to know how to measure, draw, and calculate bearings, and at Higher tier you may need to combine bearings with t
§Key definitions
Question:
The bearing of town B from town A is 135°. Find the bearing of town A from town B.
Answer:
The bearing of A from B is 315°.
Question 1:
Write the bearing for an angle of 7° from north.
Question 2:
The bearing of X from Y is 210°. Find the bearing of Y from X.
Question 3:
The bearing of B from A is 075°. The bearing of C from A is 140°. Find angle BAC.
§Formulas to memorise
Back bearing = bearing ± 180° (add 180° if the bearing is less than 180°; subtract 180° if it is 180° or more)
Angles on a straight line sum to 180°
Alternate angles (Z-angles) between parallel north lines are equal
Bearing of B from A — stand at A, face north, and turn clockwise until you face B. The angle you turn through is the bearing.
Back bearing — the bearing of A from B. If the bearing of B from A is θ, the back bearing is θ + 180° (if θ < 180°) or θ − 180° (if θ ≥ 180°).
Worked example
The bearing of town B from town A is 135°. Find the bearing of town A from town B.
Working:
⚠ Common mistakes
- ✗Measuring anticlockwise instead of clockwise. Bearings are always measured clockwise from north. If you measure anticlockwise, subtract your angle from 360°.
- ✗Forgetting the three-figure rule. A bearing of 45° must be written as 045°. Dropping the leading zero loses marks.
- ✗Drawing the north line in the wrong place. The north line must be drawn at the point you are measuring from, not at the destination.
- ✗Getting the back bearing wrong. Remember: add 180° if the bearing is under 180°; subtract 180° if it is 180° or over. A common error is always adding.
- ✗Not drawing parallel north lines. When working with multiple points, draw a north line at every point. These parallel lines help you find angles using alternate and co-interior angle rules.
✦ Exam tips
- →Always draw a clear diagram with north lines at every relevant point. Even a rough sketch helps you identify the angles.
- →Mark angles carefully. Use arcs to show which angle you mean — bearings questions often have several angles in the same diagram.
- →For Higher tier, be ready to use the sine rule or cosine rule in non-right-angled bearing triangles.
- →Use alternate angles between parallel north lines — this is the fastest way to find interior angles of the triangle.
- →Read the question carefully. "Bearing of B from A" means you stand at A and look towards B. Getting this the wrong way around changes the answer completely.