What is a bearing?
A bearing describes a direction. It is always measured clockwise from North and written with three figures, from 000° to 360°. For example a direction of 45° east of North is written 045°, due East is 090°, due South is 180° and due West is 270°.
Key idea
The back bearing (bearing of A from B when you know the bearing of B from A) is found by adding 180° if the bearing is less than 180°, or subtracting 180° if it is 180° or more.
Ruler-and-compass constructions
Using only a straight edge and a pair of compasses you can build accurate figures:
- Perpendicular bisector of a segment: the locus of points equidistant from the two endpoints.
- Angle bisector: the locus of points equidistant from the two lines that form the angle.
Worked example
A ship sails from A to B on a bearing of 070°, then from B to C on a bearing of 160°. Find the angle ABC. The back bearing of A from B is 070° + 180° = 250°. Angle ABC = 250° − 160° = 90°.
Loci
A locus is the set of all points obeying a rule. The locus of points a fixed distance r from a point is a circle of radius r; the locus a fixed distance from a line is a pair of parallel lines.
Bearings problems are usually solved on an accurate scale drawing. Choose a sensible scale (for example 1 cm to 10 km), draw a North line at each point, measure each bearing with a protractor turning clockwise, then measure the required length and convert it back using your scale.