Year 7 Interactive Maths - Second Edition

Bearings

A directional compass is shown below. It is used to find a direction or bearing .

[‰æ‘œ:A compass with markings at 10 degree intervals]

The four main directions of a compass are known as cardinal points. They are north (N), east (E), south (S) and west (W). Sometimes, the half-cardinal points of north-east (NE), north-west (NW), south-east (SE) and south-west (SW) are shown on the compass. The above compass shows degree measurements from 0�[ to 360�[ in 10�[ intervals with:

• north representing 0�[ or 360�[
• east representing 90�[
• south representing 180�[
• west representing 270�[

When using a directional compass, hold the compass so that the point marked north points directly away from you. Note that the magnetic needle always points to the north.

Bearing

The true bearing to a point is the angle measured in degrees in a clockwise direction from the north line. We will refer to the true bearing simply as the bearing.

[‰æ‘œ:The bearing or true bearing of P and Q is shown]

For example, the bearing of point P is 065ƒR which is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the centre of the compass at O with the point P (i.e. OP).

The bearing of point Q is 300ƒR which is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the centre of the compass at O with the point Q (i.e. OQ).

Note:

The bearing of a point is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the centre of the compass with the point.

A bearing is used to represent the direction of one point relative to another point.

For example, the bearing of A from B is 065ƒR. The bearing of B from A is 245ƒR.

[‰æ‘œ:The relative bearings of A and B are shown]

Note:

• Three figures are used to give bearings.
• All bearings are measured in a horizontal plane.

Example 10

State the bearing of the point P in each of the following diagrams:

Solution:

a. Mark the angle in a clockwise direction by indicating the turn between the north line and the line joining the centre of the compass to the point P.

The bearing of point P is 048�[.

b. Mark the angle in a clockwise direction by indicating the turn between the north line and the line joining the centre of the compass to the point P.

The cardinal point S corresponds to 180�[. It is clear from the diagram that the required angle is 60�[ larger than 180�[. So, the angle measured in a clockwise direction from the north line to the line joining the centre of the compass to point P is 180�[ + 60�[ = 240�[.

So, the bearing of point P is 240�[.

c. Mark the angle in a clockwise direction by indicating the turn between the north line and the line joining the centre of the compass to the point P.

The cardinal point S corresponds to 180�[. It is clear from the diagram that the required angle is 40�[ less than 180�[. So, the angle measured in a clockwise direction from the north line to the line joining the centre of the compass to point P is 180�[ ? 40�[ = 140�[.

So, the bearing of point P is 140�[.

d. Mark the angle in a clockwise direction by indicating the turn between the north line and the line joining the centre of the compass to the point P.

The cardinal point W corresponds to 270�[. It is clear from the diagram that the required angle is 20�[ larger than 270�[. So, the angle measured in a clockwise direction from the north line to the line joining the centre of the compass to point P is 270�[ + 20�[ = 290�[.

So, the bearing of point P is 290�[.

Direction

The conventional bearing of a point is stated as the number of degrees east or west of the north-south line. We will refer to the conventional bearing simply as the direction.

To state the direction of a point, write:

• N or S which is determined by the angle being measured
• the angle between the north or south line and the point, measured in degrees
• E or W which is determined by the location of the point relative to the north-south line

[‰æ‘œ:The conventional bearing or direction of A, B, C and D is shown]

E.g. In the above diagram, the direction of:

• A from O is N30ƒRE.
• B from O is N60ƒRW.
• C from O is S70ƒRE.
• D from O is S80ƒRW.

Note:

N30ƒRE means the direction is 30ƒR east of north.

Example 11

Describe each of the following bearings as directions.
a. 076�[
b. 150�[
c. 225�[
d. 290�[

Solution:

a. The position of a point P on a bearing of 076�[ is shown in the following diagram.

The position of the point P is 76�[ east of north. So, the direction is N76�[E.

b. The position of a point P on a bearing of 150�[ is shown in the following diagram.

The position of the point P is 180�[ ? 150�[ = 30�[ east of south. So, the direction is S30�[E.

c. The position of a point P on a bearing of 225�[ is shown in the following diagram.

The position of the point P is 225�[ ? 180�[ = 45�[ west of south. So, the direction is S45�[W.

d. The position of a point P on a bearing of 290�[ is shown in the following diagram.

The position of the point P is 360�[ ? 290�[ = 70�[ west of north. So, the direction is N70�[W.

Key Terms

directional compass, cardinal points, true bearing, bearing, direction, conventional bearing