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4.2 I) Bearing – Part 3
4.2 I) Bearing – Part 3
We are going to have one more bearings example in this section. The example will combine bearings with scale diagrams.
Example 1
3 towns are located near one another. Here is some information about the towns:
Complete the following questions:
3 towns are located near one another. Here is some information about the towns:
- The bearing of B from A is 030°.
- The distance between A and B is 30 miles.
- Town C is 40 miles south of town B.
Complete the following questions:
- Draw a scale diagram of the 3 towns using the scale 1 cm = 5 miles. Include lines to show your working.
- What is the distance between town A and town C?
- What is the bearing of town A from town C?
Part 1
The first part of this question asks us to draw a scale drawing, and we are told that the scale is 1 cm = 5 miles.
I am going to start by working with the first piece of information that we are given, which is that the bearing of B from A is 030°. As the bearing is being measured from A, I am going to start by making a dot where A is and drawing a north line.
The first part of this question asks us to draw a scale drawing, and we are told that the scale is 1 cm = 5 miles.
I am going to start by working with the first piece of information that we are given, which is that the bearing of B from A is 030°. As the bearing is being measured from A, I am going to start by making a dot where A is and drawing a north line.
The bearing is 030° and we measure the bearing clockwise from the north line. The working is shown below. I am going to make a mark where the bearing of 030° would be.
We are told that the distance between town A and town B is 30 miles. The scale that we are using is 1 cm = 5 miles. In order to convert 30 miles into cm on the scale drawing, we divide by 5. The working is shown below.
The distance between town A and town B on our diagram is 6 cm and we have the bearing. Therefore, we measure 6 cm from A along the bearing that we have marked. The outcome is given below.
The final piece of information that we are given in the question is that town C is 40 miles south of town B. As town C is south of town B, town C will be directly below town B. We now need to work out how far it will be below town B on the scale diagram. The scale is 1 cm = 5 miles and the distance between the two towns is 40 miles. We convert the miles into cm on the scale drawing by dividing by 5. The working is shown below:
This means that we are drawing a 8 cm line that goes directly down from B. The working is shown below:
The final diagram is shown below.
Part 2
The second part of the questions asks us to work out the distance between town A and C. We answer this question by measuring the distance between the two towns on our diagram. We then use the scale to convert the distance on the diagram to the distance in real life.
On my scale diagram, the distance between A and C is 4.1 cm.
The second part of the questions asks us to work out the distance between town A and C. We answer this question by measuring the distance between the two towns on our diagram. We then use the scale to convert the distance on the diagram to the distance in real life.
On my scale diagram, the distance between A and C is 4.1 cm.
We now need to convert 4.1 cm on the scale diagram into miles in real life. The scale that we used for this question is 1 cm = 5 miles. We are able to convert cm on the scale diagram to miles by multiplying by 5.
Therefore, the distance between town A and town C is 20.5 miles.
There will be a range of acceptable answers for questions like this, so do not worry if you get an answer that is slightly above or below 20.5 miles.
There will be a range of acceptable answers for questions like this, so do not worry if you get an answer that is slightly above or below 20.5 miles.
Part 3
The final part asks us to find the bearing of town A from town C.
The bearing that we are looking for is shown on the diagram below.
The final part asks us to find the bearing of town A from town C.
The bearing that we are looking for is shown on the diagram below.
This bearing is greater than 180°. Therefore, we find the bearing by measuring the angle between the end of the bearing and the north line. We then take this angle off of 360° (we take this angle off 360° because 360° is the number of degrees in a full circle).
The angle between the end of the bearing and the north line is 47°. The working is shown below.
The angle between the end of the bearing and the north line is 47°. The working is shown below.
The next step is to take this angle away from 360°.
Therefore, the bearing of town A from town C is 313°.