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## 1. Measured from North .

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**Bearings**360/000o N N N N 60o 270o 090o W W W W E E E E S S S S 180o 145o 315o 230o 1.Measured from North. 060o 2.In a clockwise direction. 3.Written as 3 figures. 315o 230o 145o**360/000o**350o 020o N 315o 045o NW NE 290o 080o 270o 090o W E 250o 110o SW SE 225o 210o 135o 160o S 180o Bearings Use your protractor to measure the bearing of each point from the centre of the circle. A 360o protractor is used to measure bearings.**N**030o 330o 045o 315o 290o 075o 110o 250o 135o 225o 170o 200o 360/000o Estimate the bearing of each aircraft from the centre of the radar screen. 090o E 270o W Glasgow Air Traffic Controller Glasgow Control Tower 180o S**N**360/000o 010o 7 325o 040o Estimate the bearing of each aircraft from the centre of the radar screen. 8 310o 1 ACE Controller contest 060o 11 12 4 280o 2 090o E 270o W 3 5 Air Traffic Controller 250o 10 Control Tower 9 120o 235o 6 195o 155o 180o S**Bearings**Measuring the bearing of one point from another. N To Find the bearing of B from A. B A 060o 1.Draw a straight line between both points. 2.Draw a North line at A. 3.Measure the angle between.**Bearings**Measuring the bearing of one point from another. N To Find the bearing of A from B. B A 1.Draw a straight line between both points. 240o 2.Draw a North line at B. 3.Measure angle between.**Bearings**Measuring the bearing of one point from another. N N 060o B How are the bearings of A and B from each other related and why? 240o A**Bearings**Measuring the bearing of one point from another. To Find the bearing of Q from P. N P Q 118o 1.Draw a straight line between both points. 2.Draw a North line at P. 3.Measure angle between.**Bearings**Measuring the bearing of one point from another. To Find the bearing of P from Q. N P Q 298o 1.Draw a straight line between both points. 2.Draw a North line at Q. 3.Measure angle between.**Bearings**Measuring the bearing of one point from another. N N 298o P 118o Q How are the bearings of A and B from each other related and why?**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. Thank You 300o Airfield (B) 050o 306.7 MHZ UHF Airfield (A) 283.2 MHZ UHF Bearings: Fixing Position**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 170o 255o Airfield (B) 306.7 MHZ UHF Thank You**1. Find the position of a point C, if it is on a bearing of**045ofrom A and 290ofrom B. C D B A 2. Find the position of a point D if it is on a bearing of 120ofrom A and 215o from B.**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**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**A**50M B 160° 110° 20M 20° C 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. θ Know 2 sides and opposite angle cosine rule b a) 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**E**36° L 20M 43° D 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 Know only 1 side but not the opposite angle Know 1 side and all angles sine rule 101° e**22 m**35 m 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 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**J**26o L 1800 m 100o T V 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 Solution:JV = 3321.912495LJ2=18002+3321.9124952-2(1800)(3321.912495)cos100oLJ = 4043.728627Time = 39.2 minTime reached=1930