Bearings and Scale Drawings
Use three-figure bearings and back bearings, choose instructions for scale-drawing route legs, and convert between stated drawing lengths and real distances.
What a learner can do afterwards
- Write three-figure bearings and calculate them from stated directions or angles, including bearings greater than 180 degrees
- Find the back bearing of a stated direction and justify the calculation
- Choose scale-drawing instructions for route legs, convert between stated drawing and real lengths, and distinguish route length from direct separation
1 · Read
A bearing gives the direction of one point from another. Measure clockwise from north at the starting point. On these flat plans, north lines are parallel. Use whole-degree bearings from 000 to 359, written with three figures: 8 degrees becomes 008 degrees. North is 000 degrees, east is 090, south is 180 and west is 270. A full turn of 360 degrees points north again.
For the bearing of A from B, draw north through B. Put the protractor's centre at B and zero on north. Read clockwise towards A. For a bearing past 180 degrees, measure the smaller angle anticlockwise from north, then subtract it from 360. For example, 40 degrees anticlockwise gives 320 degrees clockwise. A clockwise turn from an existing heading adds to its bearing; subtract 360 if the total reaches 360 or more.
A back bearing points along the same line in the opposite direction, half a turn away. Below 180 degrees, add 180. At 180 degrees or above, subtract 180. For example, 110 + 180 = 290, and 280 − 180 = 100. South, 180 degrees, reverses to north, 000 degrees. Adding 180 and then subtracting 360 when needed also works. Write the final bearing with three figures.
A scale links drawing length and real length. At 1 cm to 2.5 km, a 10 km leg is drawn as 10 ÷ 2.5 = 4 cm. Divide real kilometres by kilometres per centimetre to find drawing centimetres. Multiply drawing centimetres by kilometres per centimetre to find real kilometres. To find an unknown scale, divide real kilometres by drawing centimetres: 10 ÷ 4 = 2.5 km per centimetre.
To draw a route leg, mark its start and draw north through it. Mark the bearing clockwise from north, then rule the scaled length. For a bearing past 180 degrees, you can mark 360 minus the bearing anticlockwise from north. Start each new leg at the previous endpoint, with a parallel north line. Measure each bearing from north, not the previous leg. Add leg lengths for distance travelled. For direct distance, join the start and finish, measure, then use the scale.
Enlarging a drawing changes its printed scale. If every drawing length doubles, the real distance stays the same, so each new centimetre represents half as much. Divide the old kilometres per centimetre by the enlargement factor. A drawing using 1 cm to 6 km becomes 1 cm to 3 km after doubling. Use the new scale with measurements on the enlarged copy.
Measure clockwise from north at the starting point. Write three figures. Reverse by 180 degrees. Use the scale to convert lengths. Start each new leg at the previous endpoint.
This lesson and its practice material were written for this dataset.
These readings, questions and flashcards were written for this dataset. Corpus records were studied for scope and question design; their text was not copied or adapted.
More to read
Where a bearing starts
The words 'A from B' tell you where to stand: at B, looking towards A. Draw north through B. Measure clockwise from that north line towards A.
Write whole-degree bearings with three figures. A direction 7 degrees clockwise from north is 007 degrees. In these tasks, north is 000 degrees. East is 090, south is 180 and west is 270.
A semicircular protractor can help with a bearing greater than 180 degrees. Measure the smaller angle anticlockwise from north, then subtract it from 360 degrees. If that smaller angle is 50 degrees, the clockwise bearing is 360 − 50 = 310 degrees.
On a flat plan with parallel north lines, looking back along the same line reverses the direction by 180 degrees. Add 180 when the original bearing is below 180; otherwise subtract 180. At exactly 180 degrees, the reverse direction is north, written 000 degrees.
Drawing a route one leg at a time
A route description gives each leg a bearing and a distance. Use one scale for the whole drawing. Work out the drawing lengths before using your ruler.
Suppose a route starts at S, goes 5 km on a bearing of 030 degrees, then goes 7 km on a bearing of 120 degrees. At 1 cm to 1 km, the legs are drawn as 5 cm and 7 cm.
Mark S and draw north through it. Put the protractor's centre at S and align zero with north. Mark 030 degrees clockwise, then draw the first leg 5 cm long. Call its endpoint T.
Draw north through T, parallel to the first north line. From this new north line, mark 120 degrees clockwise. Draw the second leg 7 cm long. Its bearing is measured from north at T, not from the previous leg.
The travelled route is 5 + 7 = 12 km. For the direct distance from S to the finish, join those endpoints and measure the joining line. Convert that measurement using the drawing's scale.
Checking the scale on a copied drawing
At a scale of 1 cm to 6 km, a 2 cm line represents 12 km. If a copy makes every drawing length three times as long, this line becomes 6 cm. It still represents the same 12 km.
The enlarged copy uses 1 cm to 2 km, because 12 ÷ 6 = 2. You can also divide the old kilometres-per-centimetre value by the enlargement factor: 6 ÷ 3 = 2.
Use a measurement and scale from the same copy. Applying the old scale to the enlarged line would give 6 × 6 = 36 km. That would change the calculated journey even though the real route has not changed.
Check the scale whenever a drawing is enlarged or reduced. A longer printed line does not by itself mean a longer real journey.
2 · Watch
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Where it sits
Where this leads
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