Bearings

MathsDirect

You should already be familiar with bearings, so this section is just a reminder.

Bearings are a standardized way of expressing direction, using North as a basis. The obvious benefit of this, is in navigation, allowing you to be clear about directions, regardless of where you are, or more importantly, the direction that you are pointing in.

Bearings are always measured in a clockwise direction, from North and are generally phrased in the form," the bearing of A from B is 045^o". This means that you start at B and travel at an angle of 45^o, to reach A.

A bearings question will generally require you to first establish some triangles and then use trigonometry (possibly the sine/cosine rules) to find distances or bearings.

Example

A ship sails from a point A, 20km on a bearing of 120^o to a point B and then sails for 30 km on a bearing of 225^o to a final point C. Find the distance of C from A and the bearing of C from A.

First draw a diagram

We can calculate the acute angle ABC. The obtuse angle is 225^o and the acute angle adjacent to the north line must be 60^o (since the north lines must be parallel).

The acute angle ABC is 75^o.

We can therefore draw the triangle ABC

To find the length AC we must use the cos rule

To find the bearing of C from A, the easiest method is to find the angle CAB. We can do this using the sine rule.

It is essential that for your calculation, you use the accurate length of AC that you got on the calculator. If you use the rounded version (31.5) then your answer will probably not be accurate. Obviously you can write the rounded version in your working.

Therefore, the bearing of C from A is 120 + 67.1

Bearing of C from A is 187.1^o

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