CHAPTER SEVEN

Chapter 7: BEARINGS

Learning objectives

By the end of this topic, the learners should be able to

• Know the compass points

• Describe the direction of a place from a given point using compass points

• Describe the bearing of a place from a given point

• Apply bearings in real life situations

• Choose and use an appropriate scale to make an accurate drawing

• Differentiate between a sketch and a scale drawing

There are many situations in which you might need to describe your position and direction of travel. In mathematics, we use more precise ways to describe position and direction of travel and this is done by use of bearings.

Bearings have many applications in our everyday lives such as in the fields of engineering .i.e Builder architects, sailors and surveyors all use direction and angles in their work. Therefore in this topic you will learn how to tell the bearing of a point from a given point and also determine accurately the distance between two points.

7.1 Compass directions

The four cardinal(main) directions are North (N), East (E), South (S), West (W). The four intercardinal (or ordinal) directions are formed by bisecting the angle of the cardinal directions:

North-east(NE), South-east(SE), South-west(SW) and North-west(NW)

7.1 Exercise Set

The map below shows part of Taibah international school environment. Use it to answer the questions below.

1. What is East of the Office?

2. What is NW of office ?

3. What is SE of boys dormitory and E of classroom?

4. Draw a compass direction at the office and identify the directions of each of the places shown

on the map

7.2 Angles and Turns

An Angle is a measure of rotation or turn. A turn is to rotate about a point. A turn can be

described as a quarter turn, Half turn, three -quarter turn or a complete turn. This can either be

done clockwise or anticlockwise. Below is how one can turn clockwise

NOTE

• Turning from N to S is 180° clockwise or anticlockwise.

• Turning from N to NW is 315° clockwise (or 45° anticlockwise).

• Turning from NE to E is 45° clockwise (or 315° anticlockwise)

• 1 right angle = 90°

7.3 Identifying the angles in relation to the compass direction

Activity : Make the following turns and in each case state the size of the angle you have turned through.

1. Turn from N to S anticlockwise

2. Turn from NE to SE clockwise

3. Turn clockwise from NE to E

4. Turn anti clockwise from NE to SW

5. Turn clockwise from E to NW

6. Turn from S to NE clockwise

EXAMPLE

1. What angle do you turn through if you turn:

(a) from NE to NW anticlockwise?

The angle turned through is 090° or ¼turn

(b) from E to N clockwise?

The angle turned through is 270°or ¾turn

(c) from SE to NW clockwise?

The angle turned through is 180° or ½turn

7.2 Exercise Set

1. What angle do you turn through if you turn clockwise from:

(a) N to E?

(b) W to NW?

(c) SE to NW?

(d) NE to N?

(e) W to NE?

(f) S to SW?

(g) S to SE?

(h) SE to SW?

(i) E to SW?

2. In what direction will you be facing if you turn:

(a) 180° clockwise from NE?

(b) 90° clockwise from SW?

(c) 45° clockwise from N?

(d) 225° clockwise from SW?

(e) 135° anticlockwise from N?

(f) 315° clockwise from SW?

3. The sails of a windmill complete one full turn every 40 seconds.

(a) How long does it take the sails to turn through:

i. 180°  ii. 90°  iii. 45°  iv. 270° 

(b) What angle do the sails turn through in:

i. 30 seconds? ii. 15seconds? iii. 25 seconds?

7.4 Bearings

• Bearings are a more precise way of describing a direction .i.e. They show the direction of one-point relative to another point.

• A bearing is an angle measured clockwise from the north line

• In bearings angles are always measured from the North

• Bearings are stated using three digits. Thus 45° is written as 045° 

• The north line represents a bearing of 000° 

• The bearing of N130°E means an angle of 130° measured from N towards E

EXAMPLE

1. What is the bearing of B from A

The bearing of B from A is 060° 

2. What is the bearing of NW

The bearing of NW is 315° in the clockwise direction

Activity : Estimating bearings of some places within the school compound.

Draw a sketch of your school and estimate the bearings of each building found in the School and the sports grounds .i.e offices, classrooms, laboratory, kitchen, library e.t.c

NOTE

• Your compass direction must be drawn on the administration block

• All bearings must be stated using three digits.

• All bearings are measured in a horizontal plane.

7.3 Exercise Set

1. Find the bearing of each of the following directions:

(a) NE

(b) SE

(c) S

(d) SW

(e) E

(f) W

2. Find the bearing of each of the following directions:

(a) N60°E

(b) S60°E

(c) N90°W

(d) S50°W

(e) N30°W

(f) N45°E

3. Draw a scale diagram to show the position of a ship which is 270 km away from a port on a bearing of 110°.

4. The bearing of Buikwe from Lugazi in a class is 120°. What is the bearing of Lugazi from Buikwe in the class

5. A plane leaves Entebbe airport on a bearing of North East to Karamoja. What is the bearing of Entebbe from Karamoja.

6. The diagram shows the positions of two ships, A and B.

(a) What is the bearing of ship A from ship B ?

(b) What is the bearing of ship B from ship A ?

7. The map of a school is shown below: What is the bearing from the Office, of each place shown on the map?

8. An aeroplane flies from Entebbe to mbale on a bearing of 044° . On what bearing should the pilot y, to return to Entebbe from Mbale?

9. On four separate occasions, a plane leaves Entebbe airport to y to a different destination.

The bearings of these destinations from Entebbe airport are given below.

Draw a compass direction to show the direction in which the plane ies to each destination.

10. A ship sails NW from Entebbe to take supplies to Portbell. On what bearing must it sail to return from the Portbell to the Entebbe?

11. If A is north of B, C is south east of B and on a bearing of 1600 from A, and the bearing of:

(a) A from B, (b) A from C, (c) C from B, (d) B from C.

7.5 Scale Drawings

Using bearings, scale drawings can be constructed to solve problems. This involves drawing accurate drawings and showing clearly the directions.

EXAMPLES

1. A ship sails 20 km North east, then 18 km south, and then stops.

(a) Draw a scale drawing to show the routes of the ship

(b) How far is it from its starting point when it stops?

(c) On what bearing must it sail to return to its starting point?

The path of the ship can be drawn using a scale of 1 cm for every 2 km, as shown in the diagram.