Geometry & measures · Bearings
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Bearings & back bearings
The three rules of a bearing, measuring from North at each new point, the ±180° back-bearing rule, and combining bearings with right-angled trigonometry to find distances and directions.
Geometry & measures · Bearings
Bearings & back bearings
The three rules of a bearing, measuring from North at each new point, the ±180° back-bearing rule, and combining bearings with right-angled trigonometry to find distances and directions.
Why it works
A bearing has exactly three rules. It is measured- from North,
- clockwise,
- and written with three figures — so is written and
The three-figure rule is not decoration: dropping the leading zero loses the accuracy mark on its own.
The North line moves with you. The bearing of from is measured at , from the North line drawn at . The bearing of from is measured at , from a different North line. Reading "the bearing of from " backwards is the classic misread — the point after "from" is where you stand and where the North line goes.
Back bearings differ by 180°. All the North lines are parallel, so the two bearings along one line are co-interior/alternate partners:
The choice keeps the answer in the range –. So the back bearing of is , and the back bearing of is .
Bearings questions are usually trigonometry in disguise. Sketch the journey, mark the North line at each point, then hunt for the right-angled triangle — often by dropping a perpendicular. Use the parallel North lines with alternate and co-interior angles to convert bearings into the interior angles of that triangle. Once it's a triangle with an angle and a side, it's SOHCAHTOA (or Pythagoras) as usual.
Convert back to a bearing at the end. Trigonometry gives you an angle inside the triangle; the answer must be measured from North, clockwise. Add or subtract from , , or as the sketch requires, then write three figures. A quick sanity check: does your bearing point into the right quadrant of the compass?