Bearings and navigation triangles

A bearing is measured clockwise from north at the starting point. Whole-degree bearings use three digits: north \(000^\circ\), east \(090^\circ\), south \(180^\circ\), west \(270^\circ\). “Bearing of B from A” places the north line at A.

Example

From \(O\), \(A\) is 4 km away on bearing \(030^\circ\), and \(B\) is 6 km away on bearing \(090^\circ\). Thus \(\angle AOB=60^\circ\) and \(AB=\sqrt{4^2+6^2-2(4)(6)\cos60^\circ}=\sqrt{28}\text{ km}\approx5.29\text{ km}\).

Reversing a bearing adds or subtracts \(180^\circ\) to give a value from \(000^\circ\) to below \(360^\circ\). The bearing of \(O\) from \(A\) is \(210^\circ\). Bearings at different starting points cannot simply be subtracted; first use the parallel north lines to find the triangle’s interior angle.