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17.2 Making scale drawings

17.2 Making scale drawings

You can use bearings in scale drawings to help you solve problems.
When you make a scale drawing, always measure all the lengths and The scale on a map is often
angles accurately. much bigger than the scale
on a scale drawing, because

Scales are also used on maps. Maps o%en have scales such as 1 : 50 000 maps represent areas that are
or 1 : 800 000. When you convert between a distance on a map and the very big, such as countries.
actual distance you need to convert between units such as centimetres
and kilometres.

Worked example 17.2

a A ship leaves harbour and sails 120 km on a bearing of 085°. It then sails 90 km on a bearing of 135°.
i Make a scale drawing of the ship’s journey. Use a scale of ‘1 cm represents 10 km’.
ii How far and on what bearing must the ship now sail to return to the harbour?
b A map has a scale of 1 : 50 000.
i On the map a footpath is 12 cm long. What is the length, in kilometres, of the footpath in real life?
ii In real life a road is 24 km long. What is the length, in centimetres, of the road on the map?

a i N First, draw a north arrow and measure a bearing of 085°.
N
120 ÷ 10 = 12, so draw a line 12 cm long to
represent the fi rst part of the journey. Now draw another
85° 135° north arrow at the end of the fi rst line, and measure a
Harbour 12 cm
9 cm bearing of 135°. 90 ÷ 10 = 9, so draw a line 9 cm long
to represent the second part of the journey.
Ship
ii N Draw a straight line joining the ship to the harbour and
N
measure the length of the line, in centimetres.
Multiply by the scale to work out the distance the ship
85° 135° N has to sail.
Harbour 12 cm
9 cm Draw a north arrow from the position of the ship and
19.1 cm measure the angle, to give the bearing on which the
Ship
286° ship needs to sail to return to the harbour.
Distance: 19.1 × 10 = 191 km
Bearing: 286°
b i 12 × 50 000 = 600 000 cm Multiply by the scale to get the real-life distance in centimetres.
600 000 cm ÷ 100 = 6000 m Divide by 100 to convert from centimetres to metres.
6000 m ÷ 1000 = 6 km Divide by 1000 to convert from metres to kilometres.
ii 24 km × 1000 = 24 000 m Multiply the real-life distance by 1000 to convert from
24 000 m × 100 = 2 400 000 cm kilometres to metres, then by 100 to convert from metres to
2 400 000 ÷ 50 000 = 48 cm centimetres. Divide by the scale to get the distance on the
map, in centimetres.

) Exercise 17.2

1 A ship leaves harbour and sails 80 km on a bearing of 120°. It then sails 100 km on a bearing of 030°.
a Make a scale drawing of the ship’s journey. Use a scale where 1 cm represents 10 km.
b How far must the ship now sail to return to the harbour?
c What bearing must the ship now sail on, to return to the harbour?

162 17 Bearings and scale drawing