Topic 7: Bearings

By the end of this topic, you will be able to:

1. identify the compass points
2. describe the direction of a place from a given point using compass points
3. describe the bearing of a place from a given point
4. apply bearings in real life situations choose and use appropriate scale to make an accurate diagram
5. differentiate between sketch and a scale drawing

Keywords

• bearings
• compass
• sketch
• scale drawing
• sketch

Introduction

How are pilots able to fly aircraft to destinations without roads? There are no physical roads on oceans and lakes but still sailors can locate their destinations. Using the compass, you can locate the direction of a place relative to the cardinal geographic points. In this topic therefore, you will learn about bearings and how they help us solve daily life challenges.

Knowing Compass Points

Activity 7.1 Knowing compass points (work in groups)

What you need: ash and sand.

What to do:

1. Get outside the classroom and draw a compass direction of 8 points.

2. Let 4 Learners stand on the four cardinal points and 4 others on the minor points.

3. Identify the points by name of your friend and the exact point where the person is standing.

Activity 7.2 Stating the compass points (work in groups)

What you need: notebook and pen.

What to do:

1. Study the illustration below and state the compass points of the followin places from the canteen.

a) Kitchen and dinning

b) Library 78

c) Main hall

d) Toilet

e) Water tank

f) Forest park

g) Basketball court

h) Math garden

Describing Direction of a Place from a given Point

What direction do you face while heading home from school? In this section, you will describe the direction of a place from a given point.

The bearing divides directions into quadrants of 90°. north and south are the dominant directions as shown. Therefore, the direction of a point is the number of degrees to the east or west of north or south. SE S

Example (Discuss in groups)

2. Akello, Opio, Achen and Orwal are from the same family. They study from different schools. Akello is at Kako S.S (K), Opio is at Gulu High School (G), Achen at Mary Hill High School (M) and Orwal is at Bale S.S (B) as indicated by the compass points below. Describe the direction of their schools from the centre O.

Describing Bearing of a Place from a given Point

If Tom is facing North and turns clockwise to face East, then Tom is turning clock through an angle from the North. Therefore, a bearing is an angle measure degrees clockwise from the North.

Example

Exercise 7.2

1. Ivan is facing North. He turns clockwise to face South. Which angle has he

2. Nyakato is facing East. She turns clockwise to face South West. Which angle has she turned through?

3. Mark (M) is planning to visit her friends Tom (T), Grace (G) and Alexa (A) during the holiday. Use the compass points below to describe the bearing of:

Applying Bearing in Real Life Situations

Imagine you are travelling to Kampala for the first time, what comes to your mind? Getting lost? Finding your way around? You need the knowledge of bearing to determine the direction and distance of places. Stoxton

Example

Mark travelled from Fort Portal to Kabale to visit Lake Bunyonyi. He used the night bus and found himself in Kisoro the following day. Fort Portal is on a bearing of 025° from Kabale and about 600 km, while Kisoro is about 100 km to the west of Kabale. If Fort Portal is at a bearing of 038″ from Kisoro,

a) sketch the locations of the three towns.

b) what is the bearing of,

i) Kabale from Kisoro?

ii) Kisoro from Kabale?

iii) Kabale from Fortpotal?

iv) Kisoro from Fort Portal?

Exercise 7.3

1. Rakai is on a bearing of 170° from Hoima. Apac is on a bearing of 065° from Hoima. Apac and Rakai are 500 km and 800 km respectively from Hoima. What is the bearing of Hoima from:

a) Apac? b) Rakai?

2. A marathon is being organised to start from Kololo airstrip to Kampala City Square. Kololo airstrip (K) is on a bearing of 075° and 3 km from the City Square (C). From the city square, they will run towards Mulago (M) for 4 km at on a bearing of 125°. What is the bearing of the:

a) City Square from Kololo? b) City Square from Mulago?

Choosing an Appropriate Scale to make Accurate Drawing

Applying Scale to get Distance

Suppose you were asked to draw a map showing the location of your home and school from the community borehole? How would you fit such a big area on a small piece of paper?

You can solve this using a scale drawing. If you have a small object, you can enlarge it and if you have a big object you can reduce it using scale drawing.

Activity 7.3 Choosing an appropriate scale to make accurate drawing (work in groups)

What you need: papers, pens, pencils, measuring tape or metre rule.

What to do: Measure the dimensions of your classroom using a measuring tape or a metre rule.

Sketch the dimensions of your class.

Use an appropriate scale to draw the classroom accurately.

Example (Discuss in groups)

The distance from Kampala to Mbarara is 270 km. If 1 cm represents 10 km, what is the distance from Kampala to Mbarara in cm.

Exercise 7.4

1. Find the distance on a map if 1 cm represents 10 km on the ground.

a) 100 km b) 555 km c) 130 km

2. What is the actual distance on ground represented by the following cm if 1 km represents 100cm,

a) 120 cm d) 495 cm

Scale Drawing

Example (Discuss in groups) Alele studies at Agago high school. The market is 200 km from his home on a bearing of 078°. The school is 500 km from the market on a bearing of 135°. Sketch

a) Draw a sketch to represent the 3 places. -School b) Using an appropriate scale, draw an accurate diagram to represent the location of the market, school and home. c) Find the: i) distance of Alele’s home from school. ii) bearing of the school from Alele’s home. b) Scale: 1cm represents 100 km

Exercise 7.5

1. Atim and Opio stay in Portbell. They used different ships to Islands on L. Victoria; Atim used MV Uhuru while Opio used MV Kaawa. Both left portbell at the same time. MV Uhuru sailed 100 km on a bearing of 030° to Ukara Island. MV Kaawa sailed 150 km on a bearing of 120° to Rubundo Island.

a) Sketch the movements of the two boats on the same piece of paper.

b) Using an appropriate scale, draw an accurate diagram.

c) Find the:

i) bearing of Rubundo Island from Ukara Island.

ii) distance between Rubundo Island and Ukara Island.

2. Town A is 650 km from town B at a bearing of 120°. Town B is 800 km westwards of town C. Find the shortest distance from town A to town B.