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Topic 7:
BEARINGS
The diagram below shows the bearing of Kabale from where the lady is
standing.
Key words: angle, direction, bearing, scale, line, turn
By the end of this topic, you should be able to:
i) review the compass.
ii) describe the direction of a place from a given point using cardinal points.
iii) describe the bearing of a place from a given point.
iv) draw suitable sketches from the given information.
v) choose and use appropriate scale to draw an accurate drawing.
vi) differentiate between a sketch and a scale drawing.
vii) apply bearings in real life situations.
Introduction
In this topic you will learn how to tell the bearing of a point from a
given point. You will determine accurately the distance between two
points.
Sub-topic 7.1: Angles and Turns
You will need to understand clearly, what the terms such as turn, halfturn, etc. mean in terms of angles. There are 360o in one complete turn,
so the following are true.
You also need to refer to compass points: north (N), south(S), east(E),
west(W), northeast (NE), southeast (SE), southwest (SW) and northwest
(NW)
Activity 7.1: Identifying the angles in relation to the compass direction
Work in pairs
Do the following turns and in each case state the size of the angle you have turned through.
i) Turn from N to S clockwise or anticlockwise
ii) Turn from NE to SE clockwise
iii) Turning clockwise from NE to E
Example
What angle do you turn through if you turn:
(a) from NE to NW anticlockwise?
(b) from E to N clockwise?
Compare your answers with the rest of the members in class.
Solution
(a) 90° (or ¼ turn)
(b) 270° (¾ turn)
Exercise
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) 180° anticlockwise from SE?
(c ) 90° clockwise from SW?
(d) 45° clockwise from N?
(e) 225° clockwise from SW?
(f) 135° anticlockwise from N?
(g) 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°?
(b) What angle do the sails turn through in:
(i) 30 seconds? (ii) 15seconds? (iii) 25 seconds?
Sub-topic 7.2: Bearings
The bearing of a point is the number of degrees in the angle measured in a clockwise direction from North line to the line joining the centre of the compass with the point. A bearing is used to present the direction of one-point relative to another point.
Activity7.2: Estimating bearings of some places within the school compound
In groups, work in pairs and outside the classroom.
From your school flag post, estimate the bearings of each building found in the School.
Note: Three figures are used to give bearings.
All bearings are measured in a horizontal plane.
Compare your answers with the other members of the group.
Exercise
1. Find the bearing of each of the following directions:
(a) S (b) NE (c) N (d) NW
2. Find the bearing of each of the following directions:
(a) N60°E (b) N35°E (c) N90°W (d) S400E
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°.
Situation of Integration
Ajok is in Kampala City and has been told to use a car to move to Lira town. She has never gone to Lira. She has been given the map of Uganda showing routes through which she can access Lira town.
Support: Mathematical instruments, pencil, paper, pens, tracing paper and map of Uganda
Resources: Knowledge of construction of figures like triangles, lengths of sides of triangles, operations on numbers.
Task: Ajok wants to use the short distance from Kampala to Lira.
Explain how Ajok can determine the shortest distance. Using the map given to her is it possible for Ajok to use the shortest distance she has determined. Explain your answer.
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