 ## Compass Bearing And 3-Figure Bearing

Bearing is a way of defining the direction of a point using another given point as reference.

Bearing is used in fields such as navigation, land prospecting and surveying. The first step in tackling any situation involving bearing is to locate the "North" and use it as reference direction. In diagrams and maps, the North direction is almost always vertically upwards. This means the South direction is vertically downwards since it is vertically opposite to the North direction. The North-South axis is perpendicular to the East-West axis. Let us say we have 5 towns arranged as shown in the diagram below. In the diagram we are using Town A as the reference point and we have put Town A at the centre of the cardinal points of the compass. The bearing of the other towns from Town A can be expressed in two ways:

• three figure bearing
• compass bearing

### Three figure bearing

The three figure bearing of a point is the angle measured from the North of the reference point in a clockwise direction to the point.

Three figure bearing is always:

• measured from a North line in a clockwise direction.
• expressed as 3 digits, using "zero" prefixes if the angle is less than 3 digits wide. For example, 60° is expressed as 060° and 9° as 009°.

#### Example 1 Since we said the three figure bearing of a point is measured from the North in a clockwise direction. The three figure bearing of Town B from Town A = 045°.

#### Example 2 The three figure bearing of Town C from Town A is the angle measured from the North of Town A to Town C in a clockwise manner as shown in the diagram above.

Bearing = 180° – 35°

= 145°

#### Example 3 The three figure bearing of Town D from Town A is the angle measured from the North of Town A to Town D in a clockwise manner as shown in the diagram above. But since the angle of N to W in a clockwise manner is 270°, we subtract 15° from 270° to get the three figure bearing of Town D from Town A.

Bearing = 270° – 15°

= 255°

#### Example 4 The three figure bearing of Town E from Town A is the angle measured from the North of Town A to Town E in a clockwise manner as shown in the diagram above. But since the angle of a complete revolution in a clockwise manner is 360°, we subtract 50° from 360° to get the three figure bearing of Town E from Town A.

Bearing = 360° – 50°

= 010°

### Compass bearing

The compass bearing of a point is the smallest angle measured either from the North-South axis of the reference point to the point.

Compass bearing is:

• always measured either from North or South, depending on which is closest.
• measured either is a clockwise or anticlockwise direction.

#### Example 5 From the North of Town A we rotate 45° to the East to face Town B, therefore the compass bearing of Town B from Town A is N45°E.

#### Example 6 From the South of Town A we rotate 35° to the East to face Town C, therefore the compass bearing of Town C from Town A is S35°E.

#### Example 7 The angle from the South of Town A to Town D is 90° – 15° = 75° in the West direction. Therefore the bearing of Town D from Town A is S75°W.

#### Example 8 The angle from the North of Town A to Town E is 50° in the West direction. Therefore the bearing of Town E from Town A is N50°W.