Bearings and reverse directions
Start at north and turn clockwise. Keep each bearing within one turn and write three digits
- Cardinal directions These bearings locate the four main compass directions \(\displaystyle \begin{aligned}N&=000^{\circ}\\E&=090^{\circ}\\S&=180^{\circ}\\W&=270^{\circ}\end{aligned}\)
- Offsets from another direction Add a clockwise offset to that direction's bearing. Subtract an anticlockwise offset. Keep the final result within one turn
- Back bearings The two directions along the same line differ by a half-turn \(\displaystyle \begin{gathered}\text{If }0^{\circ}\leq b<180^{\circ}:\\b_{\mathrm{back}}=b+180^{\circ}\\\text{If }180^{\circ}\leq b<360^{\circ}:\\b_{\mathrm{back}}=b-180^{\circ}\end{gathered}\)
- Turns on a route A turn is measured from the direction of travel at the turning point. Name both endpoints of the leg whose bearing you want
Worked example
B lies clockwise from south of A by the stated angle. Find the bearing of B from A and the return bearing
- \(\displaystyle b=180^{\circ}+43^{\circ}\)Start at south and add the clockwise offset
- \(\displaystyle b=223^{\circ}\)This is the bearing of B from A
- \(\displaystyle r=223^{\circ}-180^{\circ}\)Subtract a half-turn because the outward bearing is at least south's bearing
- \(\displaystyle r=043^{\circ}\)The return bearing needs a leading zero
Common mistakes
Difficulty levels
Questions about this topic
Why does a small bearing need zeros?+
The convention uses three digits. A direction seven degrees clockwise from north is written 007 degrees
Can north be written as a full turn?+
A full turn reaches north again. In this topic use 000 degrees for north, with bearing values below a full turn
Which line do I reverse after a turn?+
Use the endpoints in the question. Reversing the second leg does not give the bearing back along the first leg
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 11, VCE Units 1 & 2, General Mathematics, chapter 11: Trigonometry