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1. Measured from North .

Date post: 16-Mar-2016
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Bearings. 360/000 o. N. N. N. N. 60 o. 270 o. 090 o. W. W. W. W. E. E. E. E. S. S. S. S. 180 o. 145 o. 315 o. 230 o. 1. Measured from North. 060 o. 2 . In a clockwise direction. 3. Written as 3 figures. 315 o. 230 o. 145 o. 360/000 o. 350 o. 020 o. N. 315 o. - PowerPoint PPT Presentation
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1. Measured from North . 2. In a clockwise direction. 3. Written as 3 figures. N S E W N S E W N S E W 060 o 145 o 230 o 315 o 60 o 145 o 230 o 315 o Bearings N S E W 090 o 360/000 o 270 o 180 o
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Page 1: 1. Measured from  North .

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

Page 2: 1. Measured from  North .

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

Page 3: 1. Measured from  North .

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

Page 4: 1. Measured from  North .

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

Page 5: 1. Measured from  North .

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

Page 6: 1. Measured from  North .

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

Page 7: 1. Measured from  North .

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?

Page 8: 1. Measured from  North .

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

Page 9: 1. Measured from  North .

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

Page 10: 1. Measured from  North .

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?

Page 11: 1. Measured from  North .

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

Page 12: 1. Measured from  North .

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

Page 13: 1. Measured from  North .

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

Page 14: 1. Measured from  North .

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

Page 15: 1. Measured from  North .

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

Page 16: 1. Measured from  North .

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

Page 17: 1. Measured from  North .

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)

Page 18: 1. Measured from  North .

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

Page 19: 1. Measured from  North .

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

Page 20: 1. Measured from  North .

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


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