Bearings flashcards
9 cards on Bearings: the key points, worked examples and the slips to watch. Swipe through them, or print them.
Card 1 of 9
Bearings
Three-figure bearings
What three rules does every bearing follow, and what are the compass points as bearings?
Answer it in your head, then turn the card over.
Three-figure bearings
Key points
- Measure from north.
- Turn clockwise.
- Write it with three figures: 45° is 045°, and 5° is 005°.
- North is 000°, east 090°, south 180° and west 270°.
The in-between compass points
North-east: halfway from 000° to 090°, so 045°
South-east: 090° + 45° = 135°
South-west: 180° + 45° = 225°
North-west: 270° + 45° = 315°
Watch out
Turning anticlockwise, or starting from east: always start at north and turn clockwise.
Bearings
The bearing of B from A
To measure the bearing of B from A, where do you draw the north line and put the protractor?
Answer it in your head, then turn the card over.
The bearing of B from A
Key points
- The point after "from" is where you stand: draw the north line at A.
- Join A to B, then measure the angle clockwise from the north line round to AB.
- For a bearing over 180°, measure anticlockwise from north and take that angle from 360°.
Drawing a bearing of 290°
360° − 290° = 70°
So measure 70° anticlockwise from the north line at A.
Watch out
Drawing the north line at B when the question asks for the bearing of B from A.
Bearings
Back bearings
B is on a bearing of 070° from A. How do you find the bearing of A from B?
Answer it in your head, then turn the card over.
Back bearings
Key points
- Going back means facing the opposite way, half a turn round, so the bearings differ by 180°.
- Add 180°; if that takes you past 360°, subtract 180° instead.
- If one bearing is under 180°, the back bearing is over it.
Two back bearings
070°: 70 + 180 = 250°, so A is on a bearing of 250° from B
300°: 300 + 180 = 480 is past 360, so 300 − 180 = 120°
Watch out
Taking the bearing from 360° reflects it instead: 070° reverses to 250°, not 290°.
Bearings
North lines are parallel
How do angle facts carry a bearing at one point across to another point?
Answer it in your head, then turn the card over.
North lines are parallel
Key points
- Every north line points the same way, so the north lines at two points are parallel.
- The line joining the two points crosses both north lines.
- So alternate angles are equal and co-interior angles add to 180°.
- Write each angle on the diagram as you find it, with its reason.
B is on a bearing of 070° from A
At A, the angle from north round to AB is 70°.
Co-interior angles: at B, the angle between north and BA is 180° − 70° = 110°.
It is on the west side, so the bearing of A from B is 360° − 110° = 250°.
Watch out
An angle found inside the diagram is not a bearing yet: check it is clockwise from north.
Bearings
Drawing a journey to scale
How do you draw a journey of two or more legs as a scale drawing?
Answer it in your head, then turn the card over.
Drawing a journey to scale
Key points
- Draw a north line at the start of the first leg.
- Measure the bearing clockwise with a protractor, then mark the scaled length along it.
- Start the next leg where this one ends, with a fresh north line there.
Scale 1 cm to 2 km
A 12 km leg: 12 ÷ 2 = 6 cm on the drawing
A 9 km leg: 9 ÷ 2 = 4.5 cm
Watch out
Using the first north line for every leg: each leg needs its own north line where it starts.
Bearings
Reading the answer off a scale drawing
Once the journey is drawn, how do you find the distance and the bearing back to the start?
Answer it in your head, then turn the card over.
Reading the answer off a scale drawing
Key points
- Join the finish to the start with a ruler.
- Measure that line to the nearest millimetre, then multiply by the scale.
- For the bearing home, draw north at the finish and measure clockwise to the line.
Line home 7.3 cm, at 1 cm to 2 km
Real distance: 7.3 × 2 = 14.6 km
Bearing home: measured at the finish, not at the start
Watch out
Dividing by the scale on the way back: a length on the drawing is multiplied up to real life.
Bearings
Right-angled journeys
A journey goes due east, then due north. How do you find the direct distance and the bearing from the start?
Answer it in your head, then turn the card over.
Right-angled journeys
Key points
- East then north meet at a right angle, so the direct line is the hypotenuse.
- Pythagoras gives the direct distance.
- tan⁻¹ gives an angle inside the triangle: sketch north to turn it into a bearing.
12 km east, then 5 km north
Distance: = = 13 km
tan⁻¹ = 22.6°, measured up from the east line
Bearing from the start: 90° − 22.6° = 067.4°
Watch out
tan⁻¹ = 22.6° is measured from east, so 022.6° is not the bearing.
Bearings
How far east and how far north
A ship sails 10 km on a bearing of 040°. How do you find how far east and how far north it has gone?
Answer it in your head, then turn the card over.
How far east and how far north
Key points
- Sketch it: the 10 km leg is the hypotenuse, and 40° is the angle at the start, from north.
- The north side is next to that angle, so it uses cos.
- The east side is opposite the angle, so it uses sin.
10 km on a bearing of 040°
North: 10 × cos 40° = 7.66 km
East: 10 × sin 40° = 6.43 km
Watch out
A calculator set to radians gives answers that make no sense: check it is in degrees.
Bearings
HigherJourneys without a right angle
Two legs of a journey are not at right angles. How do you find the direct distance?
Answer it in your head, then turn the card over.
Journeys without a right angle
Key points
- Use the bearings and the parallel north lines to find the angle between the legs.
- The cosine rule then gives the direct distance.
- The sine rule finds another angle, which you turn into a bearing from north.
Formula
a² = b² + c² − 2bc cos A
7 km on 030°, then 5 km on 110°
At the turn, the bearing back to the start is 030° + 180° = 210°
So the angle between the legs is 210° − 110° = 100°
d² = 7² + 5² − 2 × 7 × 5 × cos 100° = 86.2
d = = 9.28 km
Watch out
Pythagoras needs a right angle: find the angle between the legs before you choose a rule.
Print these cards
Four cards to an A4 sheet, each the size of a standard A6 revision card.
One-sided
Each card prints on one face: the question at the top, the notes under it.
Two-sided
Questions on the front, notes on the back. Print double-sided and flip on the long edge, then cut along the lines.
Put it into practice
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