1. Measured from North.
2. In a clockwise direction.3. Written as 3 figures.
N
S
EW
N
S
EW
N
S
EW
060o
145o 230o
315o
60o
145o
230o 315o
Bearings
N
S
EW 090o
360/000o
270o
180o
Bearings
N
S
EW 090o
360/000o
270o
180o
A 360o protractor is
used to measure bearings. 020o
080o
110o
SE
135o
160o
210o
SW
225o
250o
290o
NW315
o
350o
Use your protractor to measure the bearing of each point from the centre of the circle.
NE
045o
360/000o
090o
180o
270oW E
N
S
Glasgow Air Traffic
ControllerGlasgowControl Tower
Estimate the bearing of
each aircraft from the
centre of the radar
screen.
030o
075o
045o
200o
135o
330o
225o
290o
110o250o
315o
170o
360/000o
090o
180o
270oW E
N
S
Air Traffic ControllerControl
Tower
1
2
12
10 9
8
411
7
6
53
040o
250o
280o
120o
195o
010o325o
155o
235o
310o
060o
Estimate the bearing of
each aircraft from the
centre of the radar
screen.
ACEControllercontest
Bearings
Measuring the bearing of one point from another.
1. Draw a straight line between both points.2. Draw a North line at A.
3. Measure the angle between.
N060o
To Find the bearing of B from A.
B
A
Bearings
Measuring the bearing of one point from another.
1. Draw a straight line between both points.2. Draw a North line at B.
3. Measure angle between.
N
240o
To Find the bearing of A from B.
B
A
Bearings
Measuring the bearing of one point from another.
N060o
B
A
N
240oHow are the bearings of A and B from each other related and why?
Bearings
Measuring the bearing of one point from another.
1. Draw a straight line between both points.2. Draw a North line at P.
3. Measure angle between.
N
P
Q
To Find the bearing of Q from P.
118o
Bearings
Measuring the bearing of one point from another.
1. Draw a straight line between both points.2. Draw a North line at Q.
3. Measure angle between.
N
P
Q
To Find the bearing of P from Q.
298o
Bearings
Measuring the bearing of one point from another.
N
P
Q118o
N298o
How are the bearings of A and B from each
other related and why?
A1. 2. 3.
4. 5. 6
D S
M
P
V
W
Q
T
N
B C
Bear ingsBearings are M easured1. From N orth2. Clockw ise3. Using 3 figures
Find the b e a ring s o f the fo llo w ing :1 . A fro m B 4 . M fro m N2 . C fro m D 5 . P fro m Q3 . T fro m S 6 . V fro m W
N030
060
090
120
150
180
210
240
270
300
330
360/000
W E
S
Bearings: Fixing PositionTrainee 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
Bearings: Fixing PositionTrainee 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
Thank You
170o255o
A
B
1. Find the position of a point C, if it is on a bearing of 045o from A and 290o from B.
C
2. Find the position of a point D if it is on a bearing of 120o from A and 215o from B.
D
Revision : In a non-right-angled triangle, we use Sine Rule and Cosine Rule to find the unkown.
Finding a side length
Bb
Aa
sinsin
The sine rule What do we need?The size of the opposite angleThe length of another side & it’s opposite angleOR, 2 angles and a side length.
The cosine rule What do we need?The size of the opposite angleThe length of the another 2 sidesAbccba cos2222
bB
aA sinsin
bcacbA
2cos
222
Finding an angleThe sine rule What do we need?
The length of the opposite sideThe length of another side & it’s opposite angleOR, 2 side lengths and a angle.
The cosine rule What do we need?The length of all 3 sides
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.
Example 1
Baccab cos2222
A B50M 160°
C
20M
a) b
20°
110°
110cos205022050 222 b0435842 bM8759b
Know 2 sides and opposite anglecosine rule
θ
Know all 3 sides and an opposite angle Can use cosine rule or sine ruleUse sine rule as it is easier
bB
aA sinsin
8759110sin
20sin
A
8759110sin20sin
A
18Abearing is 108° or S72°E
b)
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.
Example 2
D43° e
101°Know 1 side and all angles sine rule
Ll
Ee
sinsin
101sin20
36sine
101sin36sin20e
Me 9811
20M
E 36° L
Shortest distance opposite smallest angleKnow only 1 side but not the opposite angle
Short Quiz
Question 1:
49
106
North
A
C
B
35 m
22 m
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 mc) None of the above
Solution:(AC)2 = 352 + 222 – 2(22)(35)cos(106o)AC = 46.18962576
Area of triangle ABC = 0.5(22)(35)sin(106o)0.5(46.18962576)h = 0.5(22)(35)sin(106o)h = 16.02 m
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.
a) 1929b) 1930c) 1931
J
26o
100o1800 m
TV
L
Solution:JV = 3321.912495LJ2=18002+3321.9124952-2(1800)(3321.912495)cos100o
LJ = 4043.728627Time = 39.2 minTime reached=1930
