1. Bearings 1. Measured from North. 2. In a clockwise direction.
3. Written as 3 figures. N S E W
315o
145o
230o
315o
230o
145o

2. A 360o protractor is used to measure bearings.
Use your protractor to measure the bearing of each point from the centre of the circle. N S E W
090o
360/000o
270o
180o
350o
020o NW
315o NE
045o
290o
080o
250o SW
225o
210o
110o
160o SE
135o

3. Glasgow Air Traffic Controller
Estimate the bearing of each aircraft from the centre of the radar screen.
315o
045o
290o
075o
270o
090o E W
250o
225o
200o
170o
110o
135o
Glasgow Air Traffic Controller
Glasgow
Control Tower
180o S

4. Air Traffic ControllerW E N S
Air Traffic Controller
Control Tower
010o 1 2 12 10 9 8 4 11 7 6 5 3
325o
Estimate the bearing of each aircraft from the centre of the radar screen.
ACE
Controller
contest
040o
310o
060o
280o
250o
235o
195o
120o
155o

5. Bearings B A Measuring the bearing of one point from another.
To Find the bearing of B from A. B A
060o N
1. Draw a straight line between both points.
2. Draw a North line at A.
3. Measure the angle between.

6. Bearings B A Measuring the bearing of one point from another.
To Find the bearing of A from B. B A N
1. Draw a straight line between both points.
240o
2. Draw a North line at B.
3. Measure angle between.

7. How are the bearings of A and B from each other related and why?
Measuring the bearing of one point from another. N
060o B A
240o
How are the bearings of A and B from each other related and why?

8. Bearings P Q Measuring the bearing of one point from another.
To Find the bearing of Q from P. N
118o
1. Draw a straight line between both points.
2. Draw a North line at P.
3. Measure angle between.

9. Bearings P Q Measuring the bearing of one point from another.
To Find the bearing of P from Q. N
298o
1. Draw a straight line between both points.
2. Draw a North line at Q.
3. Measure angle between.

10. How are the bearings of A and B from each other related and why?
Measuring the bearing of one point from another. N P Q
118o
298o
How are the bearings of A and B from each other related and why?

12. Bearings: Fixing Position
Trainee pilots have to to learn to cope when the unexpected happens. If their navigation equipment fails they can quickly find their position by calling controllers at two different airfields for a bearing. The two bearings will tell the pilot where he is. The initial call on the controllers radio frequency will trigger a line on the radar screen showing the bearing of the calling aircraft.
Airfield (A)
283.2 MHZ UHF
Airfield (B)
306.7 MHZ UHF
050o
300o
Thank You

13. Bearings: Fixing Position
Trainee pilots have to to learn to be cope when the unexpected happens. If their navigation equipment fails they can quickly find their position by calling controllers at two different airfields for a bearing. The two bearings will tell the pilot where he is. The initial call on the controllers radio frequency will trigger a line on the radar screen showing the bearing of the calling aircraft.
Airfield (A)
283.2 MHZ UHF
Airfield (B)
306.7 MHZ UHF
170o
255o
Thank You

14. A B
1. Find the position of a point C, if it is on a bearing of 045o from A and 290o from B.
2. Find the position of a point D if it is on a bearing of 120o from A and 215o from B. C D

15. Finding a side length
Revision : In a non-right-angled triangle, we use Sine Rule and Cosine Rule to find the unkown.
The sine rule
What do we need?
The size of the opposite angle
The length of another side & it’s opposite angle
OR, 2 angles and a side length.
The cosine rule
What do we need?
The size of the opposite angle
The length of the another 2 sides

16. Finding an angle The sine rule What do we need?
The length of the opposite side
The length of another side & it’s opposite angle
OR, 2 side lengths and a angle.
The cosine rule
What do we need?
The length of all 3 sides

17. Example 1
A ship sails 50 nautical miles (M) due east from port A to a buoy at B, the 20M on a bearing of 160°T to port C. Find the:
a) Distance of port C from port A.
b) Bearing of port C from port A. A B
50M
160° C
20M θ
20°
110°
Know 2 sides and opposite angle
cosine rule a) b
Know all 3 sides and an opposite angle
 Can use cosine rule or sine rule
Use sine rule as it is easier b)
bearing is 108° or S72°E

18. Example 2
A plane flies due north from D with a bearing of a lighthouse L being N43°E. After flying 20M to E, the bearing of the lighthouse L is S36°E. Find which point is closest to L and the distance.
Shortest distance opposite smallest angle D
43°
Know only 1 side but not the opposite angle
20M E
36° L
Know 1 side and all angles
 sine rule
101° e

19. a) 16.2 m b) 16.1 m c) None of the above
Short Quiz
Question 1:
Tommy walks from A to C, find the distance he will be from B when he is nearest to it.
a) 16.2 m b) 16.1 m c) None of the above
35 m
22 m
Solution: (AC)2 = – 2(22)(35)cos(106o) AC =
Area of triangle ABC = 0.5(22)(35)sin(106o) 0.5( )h = 0.5(22)(35)sin(106o) h = m

20. Question 2:
A boat sailing from J to L is moving at an average speed of 1.72 m/s. If it leaves the jetty J at 18 50, find the time to the nearest minute, that it will reach the lighthouse L. J
26o
100o
1800 m T V L
a) 1929 b) 1930 c) 1931
Solution: JV = LJ2= (1800)( )cos100o LJ = Time = 39.2 min Time reached=1930