Cambridge International Mathematics

330 Trigonometry (Chapter 15)

We can measure a direction by comparing it with thetrue north direction. We call this atrue bearing.

Measurements are always taken in theclockwisedirection.

Imagine you are standing at point A, facing north. You turn

clockwisethrough an angle until you face B. Thebearing of

BfromAis the angle through which you have turned.

So, the bearing of B from A is the clockwise measure of the

angle between AB and the ‘north’ line through A.

To find the truebearing of A from B, we place ourselves at

point B and face north. We then measure the clockwise angle

through which we have to turn so that we face A. The true

bearing of A from B is 252 o.

Note: ² A true bearing is always written using three digits. For example, we write 072 orather than 72 o.

² The bearings of A from B and B from A always differ by 180 o.

You should be able to explain this using angle pair properties for parallel lines.

Example 10 Self Tutor

An aeroplane departs A and flies on a 143 ocourse for 368 km. It then changes direction to a 233 o

course and flies a further 472 km to town C. Find:

a the distance of C from A b the bearing of C from A.

First, we draw a fully labelled diagram of the flight. On

the figure, we show angles found using parallel lines.

Angle ABC measures 90 o.

a AC=

p

3682 + 472^2 fPythagorasg

¼ 598 : 5

So, C is about 599 km from A.

b To find the required angle we first need to findμ.

Now tanμ=

OPP

ADJ

=

472

368

) μ= tan¡^1

¡ 472

368

¢

) μ¼ 52 : 1 o

The required angle is 143 o+52: 1 o¼ 195 : 1 o

) the bearing of C from A is about 195 : 1 o:

E TRUE BEARINGS [8.7]

A

B

north

72°

A

B

north

252°

368 km

472 km

C

N

37°

233°

B

N

A 143°

q

In the diagram above, the bearing of B from A is 72 ofrom true

north. We write this as 72 oTor 072 o.

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Y:\HAESE\IGCSE01\IG01_15\330IGCSE01_15.CDR Friday, 21 November 2008 2:59:10 PM PETER