Bearings

Bearings are measured clockwise from north. How far round from north is east?

South is 180° from north. South-west is halfway between south and west.

Start at the north line at A and turn clockwise until you reach the line to B.

The 40° is measured anticlockwise from north. Bearings are always measured clockwise from north.

Turning clockwise from north to south is 180°. The line to B is not quite that far round.

Turning clockwise from north to south is 180°. The line to B goes further round than south.

1. Turning clockwise from north to south is 180°.
2. The line AB is a further 40° round, past south towards west.
3. 180+40=220, so the bearing of B from A is 220°.

Where must a bearing be measured from? Look at which line the 70° starts from.

1. A bearing is measured clockwise from north.
2. The 70° in the diagram is measured between the line PQ and the line pointing south.
3. So Josh measured from the wrong line. The bearing of Q from P is actually 180-70=110°.

Draw a sketch with a north line at each point. The bearing back is exactly the opposite direction.

1. The bearing from L back to B points in the opposite direction, which is a half turn (180°) away.
2. The bearing 064° is less than 180°, so add 180°: 64+180=244.
3. The bearing of B from L is 244°.

The bearing back is the opposite direction, 180° away. Adding 180° here would take you past 360°.

1. The opposite direction is 180° away from 295°.
2. 295° is more than 180°, so subtract 180°: 295-180=115.
3. The bearing of S from C is 115°.

"The bearing of B from A" is measured at A. "The bearing of A from B" is measured at B.

Part (a)

1. Stand at A, face north and turn clockwise to face B.
2. That angle is 75°, so the bearing is 075°.

Part (b)

1. Now stand at B and face A. That is the opposite direction to facing B from A.
2. The opposite direction is 180° away: 75+180=255.
3. The bearing of A from B is 255°.

Bearings start from north and turn clockwise. For the distance, each centimetre on the map stands for 3 km.

Part (a)

1. Turning clockwise from north to east is 90°.
2. The line AB is a further 28° round, past east towards south.
3. 90+28=118, so the bearing of B from A is 118°.

Part (b)

1. Each centimetre on the map represents 3 km.
2. 7.5\times3=22.5
3. The helicopter flies 22.5 km.

Work out how many lots of 5 km make 30 km. For the way back, the ship faces the opposite direction.

Part (a)

1. Each centimetre represents 5 km.
2. 30\div5=6
3. The line should be 6 cm long.

Part (b)

1. Sailing back means facing the opposite direction, which is 180° away.
2. 140+180=320
3. The ship sails back on a bearing of 320°.

Sketch a north line at L. How far is A from north, and how far is B from north?

1. Boat A is on a bearing of 300°, so the line LA is 360-300=60° anticlockwise from north.
2. Boat B is on a bearing of 040°, so the line LB is 40° clockwise from north.
3. The angle between them goes through north: 60+40=100. Angle ALB is 100°.

Draw a sketch with a north line at B. Mark the direction back to A and the direction on to C.

Part (a)

1. The bearing of A from B is the opposite direction to 125°.
2. 125+180=305
3. The bearing of A from B is 305°.

Part (b)

1. At B, the line to A is on a bearing of 305° and the line to C is on a bearing of 035°.
2. Turning clockwise from 305° up to north (360°) is 55°, then on to 035° is another 35°.
3. 55+35=90, so angle ABC is 90°.

Bearings turn clockwise from north. If B is 75° anticlockwise from north, how far is it clockwise?

1. Bearings are measured clockwise from north, but Tom turned anticlockwise.
2. A full turn is 360°, so turning clockwise from north to the line AB is 360-75=285°.
3. The correct bearing is 285°.

First use the angles in the triangle to find angle BAC. Then add it on to the bearing of B.

1. Angles in a triangle add up to 180°, so angle BAC =180-55-75=50°.
2. Turning clockwise from north to B is 70°. Turning on from B to C is another 50°.
3. 70+50=120, so the bearing of C from A is 120°.

Turning clockwise adds to the bearing and turning anticlockwise takes away. A bearing must stay between 0° and 360°.

Part (a)

1. Turning clockwise adds to the bearing: 310+85=395.
2. That is more than a full turn, so take away 360°: 395-360=35.
3. The new bearing is 035°.

Part (b)

1. Turning anticlockwise takes away from the bearing. From 035°, turning 35° anticlockwise reaches north (000°).
2. That leaves 150-35=115° more to turn anticlockwise from north.
3. 360-115=245, so the ship now sails on a bearing of 245°.

First find the bearing the boat sails on from B back towards H. Then turn 90° clockwise from that.

1. Sailing from B back towards H is the opposite direction to 072°: 72+180=252°.
2. Turning 90° clockwise adds 90° to the bearing: 252+90=342.
3. The boat now sails on a bearing of 342°.

Work out the angle between the two bearings. What does it tell you about the directions the boats sail in?

1. The difference between the bearings is 248-68=180°.
2. So the boats sail in exactly opposite directions, and P, H and Q lie on a straight line.
3. Each boat is 12 km from H, so they are 12+12=24 km apart.

First work out the bearing of A from B. Then turn back from that line through angle ABC.

1. The bearing of A from B is the opposite direction to 080°: 80+180=260°.
2. So at B, turning clockwise from the line BA on round to north is 360-260=100°.
3. Angles at a point add up to 360°. Turning clockwise from north to BC, then BC to BA (115°), then BA back to north (100°) makes a full turn.
4. 360-115-100=145, so the bearing of C from B is 145°.