Sheet № 171 · Foundation + Higher · AQA · Edexcel · OCR
Bearings and Trigonometry –
Bearings combine angle work with trigonometry and are a favourite topic on GCSE papers. You need to know how to measure, calculate, and describe bearings, and at Higher tier you must use trigonometry to find distances and angles in bearings problems.
§Key definitions
Question:
Town B is due east of Town A. What is the bearing of B from A?
Q1 (Foundation):
The bearing of Y from X is 210°. Find the bearing of X from Y.
Q2 (Foundation):
Town B is directly southwest of Town A. What is the bearing of B from A?
Q3 (Higher):
A boat sails from A on a bearing of 040° for 12 km to B. From B it sails on a bearing of 130° for 9 km to C. The angle ABC is 90°. Find the distance AC.
§Formulas to memorise
Return bearing = original bearing + 180° (if result > 360°, subtract 360°)
SOHCAHTOA for right-angled triangle problems: sin = opp/hyp, cos = adj/hyp, tan = opp/adj
PR² = 80² + 50² − 2(80)(50)cos 120°
PR² = 6400 + 2500 − 8000 × (−0.5)
PR² = 8900 + 4000 = 12900
PR = √12900 = 113.6 (1 d.p.)
The return bearing = 125° + 180° = 305°.
Worked example
Town B is due east of Town A. What is the bearing of B from A?
Working: North is straight up. Due east is a 90° clockwise rotation from north.
⚠ Common mistakes
- ✗Forgetting three figures. A bearing of 70° must be written as 070°. Losing the leading zero costs marks.
- ✗Measuring anticlockwise. Bearings are always measured clockwise from north, never anticlockwise.
- ✗Drawing north in the wrong place. You must draw a north line at the point you are measuring from, not the point you are measuring to.
- ✗Incorrect return bearings. To find the return bearing, add 180° to the original bearing. If the result exceeds 360°, subtract 360°. Do not simply subtract from 360°.
✦ Exam tips
- →Always draw a clear north arrow at each point in the problem — this makes angle identification much easier.
- →Label all known angles and sides before starting any calculation.
- →For Higher tier, be prepared to use the sine rule or cosine rule in non-right-angled bearing triangles.
- →State the three-figure bearing clearly in your final answer.
- →Use co-interior angles (add to 180°) and alternate angles to find unknown angles in bearing diagrams with parallel north lines.