1. Bearings

2. Simple Bearings
We have learnt how to find directions with a compass in primary school.
The eight directions
To describe the directions of a point relative to another point more precisely, true bearing or compass bearing may be used.

3. True Bearing
When using the true bearing, directions are measured from the north in a clockwise direction. P
clockwise
direction x°
It is expressed as x°, where 0 ≤ x < 360 and the integral part of x must consist of 3 digits.

4. The true bearings of A, B and C measured from O are
For example, A
065°
65°
120° B
273°
The true bearings of A, B and C measured from O are
, and respectively.
065°
120°
273°
The true bearing must consist of 3 digits.

5. Compass Bearing
When using the compass bearing, directions are measured from the north or the south.
It is expressed as
Nx°E,
Nx°W,
Sx°W or
Sx°E,
where 0 < x < 90. B A C D

6. For example,
The compass bearing of A from O is N26°E,
and the compass bearing of B from O is S65°W.

7. Follow-up question (a) Find the compass bearing of B from A.
(b) Find the true bearing of A from B.
Solution
(a)
The compass bearing of B from A is N A B W 65
N65°W.
(b) The true bearing of A from B is
∠CBA.
∠CBA + ∠BAD = 180° (int. ∠s, CB // DA)
∴ The true bearing of A from B is 115°.

8. Problems Involving Bearings
I walk 4 km due east from A to B,
and then walk 6 km due south to C.
If I want to return to A by the shortest route,
which direction should I take? N N
4 km A B
the shortest route
6 km C

9. With the notations in the figure, the required direction is N °W.
4 km A B
tan = BC AB
6 km
6 km
4 km =
33.7 N )
0.1
nearest
the to
(cor.
33.7 = C
So, the direction I should take is N33.7°W.

10. Follow-up question
A ship sails in the direction S36°E from A to B for 50 km. Then it sails in the direction N54°E from B to C for 120 km. (a) What is the distance between A and C?
Solution D E F
With the notations in the figure,
(a) ∵ ∠EBA = ∠DAB
(alt. ∠s, EB // AD)
= 36°
∴ ∠ABC = ∠EBA + ∠EBC
= 36° + 54°
= 90°

11. Follow-up question (cont’d)
A ship sails in the direction S36°E from A to B for 50 km. Then it sails in the direction N54°E from B to C for 120 km. (a) What is the distance between A and C?
Solution D E F
(a) Consider △ABC. 2 + = BC AB AC
(Pyth. theorem)
130 km = km
120 50 2 + =
∴ The distance between A and C is 130 km.

12. Follow-up question (cont’d)
A ship sails in the direction S36°E from A to B for 50 km. Then it sails in the direction N54°E from B to C for 120 km. (b) Find the compass bearing of A from C,
correct to 3 significant figures.
Solution D E F
(b) Consider △ABC.
tan = Ð BC AB
ACB km
120 50 = ∴

13. Follow-up question (cont’d)
A ship sails in the direction S36°E from A to B for 50 km. Then it sails in the direction N54°E from B to C for 120 km. (b) Find the compass bearing of A from C,
correct to 3 significant figures.
Solution D E F
(b)
∵ ∠FCB = ∠EBC
(alt. ∠s, CF // EB)
= 54° ∴ Ð + =
ACB
FCB
ACF +
61986 . 22 54
(cor. to 3 sig. fig.) = 6 . 76 ∴
The compass bearing of A from C is S76.6°W.