Bearings, Constructions & Scale Drawings (Cambridge (CIE) IGCSE Maths: Extended)

In triangle  = 10 cm and  = 11 cm.

Using a ruler and compasses only, construct triangle . The line  has been drawn for you.

Two towns, A and B, are shown on a map.

Measure the bearing of B from A.

Calculate the bearing of A from B.
You must show all your working.

In triangle ABC, BC = 7.6 cm and AC = 6.2 cm.  

Using a ruler and compasses only, construct triangle ABC. Leave in your construction arcs.
The side AB has been drawn for you.

The diagram shows a triangular field, ABC, on horizontal ground.

The angle BAC is equal to 82.8°.

The bearing of C from A is 210°.

i) Find the bearing of B from A.

[1]

ii) Find the bearing of A from B.

[2]

The diagram shows a field, ABCD, on horizontal ground.

The angle CAD is 35.8° and the bearing of D from A is 070°.

Find the bearing of A from C.

The diagram shows a field ABCD.
The bearing of B from A is 140°. 
C is due east of B and D is due north of C.
AB = 400m, BC = 350m and CD = 450m.

Find the bearing of D from B.

The scale of a map is 1 : 10 000 000.
On the map, the area of Slovakia is 4.9 cm².

Calculate the actual area of Slovakia.
Give your answer in square kilometres.

............................................. km²

On a map with scale 1 : 25000, the area of a lake is 33.6 square centimetres.

Calculate the actual area of the lake, giving your answer in square kilometres.   

 ........................................ km²

The diagram shows the positions of three towns, Acton (), Barston () and Chorlton ().

Barston is 8 km from Acton on a bearing of . Chorlton is 9km from Barston on a bearing of .

Find the bearing of Chorlton from Acton.
Give your answer correct to 1 decimal place.
You must show all your working.

A, B, C and D are four towns.

B is 25 kilometres due East of A.
C is 25 kilometres due North of A.
D is 45 kilometres due South of A.

Work out the bearing of B from C.

Calculate the bearing of D from B.

The diagram shows a field, ABCD, on horizontal ground. BC = 192 m, CD = 287.9 m, BD = 168 m and AD = 205.8 m.

Angle CBD = 106°.

i) The bearing of D from B is 038°.

 Find the bearing of C  from B.

[1]

ii) A is due east of B.

 Calculate the bearing of D  from A.

[5]

The diagram shows the positions of three points , and in a field.

Show that is 118.1 m, correct to 1 decimal place.

Calculate angle .

Angle ...............................................

The bearing of from is 147°. Find the bearing of 

i) from ,

[3]

ii) from .

[2]

The diagram shows the positions of three ships, and .

Ship is due north of ship .

The bearing of ship from ship is 120°

Calculate the bearing of ship from ship .
Give your answer correct to the nearest degree.

,  and  are three towns.

The bearing of  from  is 105°
The bearing of from B is 230°

The distance of  from  is 180 km.
The distance of  from  is 95 km.

Calculate the distance of  from .
Give your answer correct to 3 significant figures.

........................km

A ship sails from to and then from to .

is 12 miles from , on a bearing of 080°

is 28 miles from , on a bearing of 155°

Work out the direct distance from to .