### GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Bearings

A bearing helps us determine the direction of one point relative to another. Bearings are measured in degrees (°), with values ranging from 0° to 360°.

There are three basic rules to remember when working with bearings:

• Measured clockwise – Bearings are always measured in a clockwise direction, which ensures that they have consistent positive values ranging from 0° to 360°.
• Expressed in three digits – Bearings are represented using three digits, with leading zeros added if necessary. For example, a bearing of 45° would be represented as 045°, while a bearing of 5° would be represented as 005°. This makes it easier to read and compare bearings.
• Based on a reference direction – Bearings rely on a reference direction from which to begin, typically the north line. However, in some cases, other reference directions may be used, depending on the context. For example, when measuring the path of a vehicle relative to a road.

A protractor is typically used to measure bearings. To do so

1. Place the protractor’s centre point on the vertex where the angle is formed.

2. Align the protractor’s baseline with the reference direction (usually True North, Magnetic North, or the specific reference direction for your problem).

3. Read the bearing value from the protractor’s scale, starting from the baseline and moving clockwise around the angle being measured.

## Calculating Bearings

Let’s look at how to find the new bearing after making a turn.

Example:

Imagine a person standing at point A and facing a bearing of 045°. The person then decides to turn 90° to the left. We want to find the new bearing the person is facing after the turn.

To find the new bearing, we subtract the angle of the turn from the initial bearing:

New bearing = Initial bearing − Angle of turn

New bearing = 045° − 90°

Since the result is negative, we add 360° to find the equivalent positive bearing:

New bearing = −45° + 360° = 315°

So, the person is now facing a bearing of 315° after turning 90° to the left.