Bearings and Compass Directions

Basic Terminology

A bearing is a measurement of direction between two points. It’s calculated as an angle in degrees, measured clockwise from True North.
True North is the geographical north directly along the Earth’s rotational axis.
Compass directions, such as North (N), East (E), South (S), and West (W), are used to describe general directions.
A compass rose is a diagram that shows directions and bearings on a map. The north line represents 0° or 360°, east represents 90°, south is 180°, and west is 270°.

Using Bearings

Bearings are always given as three-digit numbers, between 000° and 360°. For instance, a bearing of 45° would be written as 045°.
To measure a bearing from one point to another, you start by pointing the 0° (north line) of your protractor towards the north, and measure the angle in the clockwise direction.
Bearings are a very useful tool in navigation, allowing for precise indications of where one location is relative to another.

Compass Directions

The main compass points are North, East, South, and West. Intermediate points are also used, such as:
- North-East (NE), lying halfway between N and E
- South-East (SE), lying halfway between S and E
- South-West (SW), lying halfway between S and W
- North-West (NW), lying halfway between N and W
The compass rose thus has eight main points: N, NE, E, SE, S, SW, W, NW. These can be further subdivided.
When giving a direction in relation to compass points, it is traditional to give the direction as a combination of these points. For example, a direction halfway between North and North-East would be described as “North-North-East”.

Bearings and Compass Directions in Mathematics

In trigonometry, you’ll often convert between bearings and angles. When converting, remember that bearings are measured from the north line clockwise, while angles in mathematics are typically measured counter-clockwise from the positive x-axis.
Problems involving bearings and compass directions often require techniques such as constructing and interpreting scale drawings, measuring and drawing angles, or using Pythagoras’ theorem and trigonometry in right-angled triangles.
In understanding compass directions and bearings, you are developing skills in spatial awareness, measurement, and direction - all key concepts in the study of geometry.

Understanding how to work with bearings and compass directions and how to apply this knowledge in mathematics can go a long way towards improving your understanding of the larger field of geometry as a whole.