Bearings
Bearings Revision
Bearings
Bearings are a way of expressing the angle between two objects. There is a specific set of rules about how bearings should be calculated and expressed.
1. Always measure bearings from the North line.
2. Always express your answers as three-figure bearings (so 60\degree would be 060\degree).
3. Always draw and measure bearings clockwise.
Understanding angles on parallel lines is required for this topic.
Skill 1: Bearings – 3 Rules
There is a specific set of rules about how bearings should be calculated and expressed.
1. Always measure bearings from the North line.
2. Always express your answers as three-figure bearings (so 60\degree would be 060\degree).
3. Always draw and measure bearings clockwise.
![measuring bearings example](https://mmerevise.co.uk/app/uploads/2020/09/Bearings-Example1.png)
Example 1: Measure a Bearing
Find the bearing of \textcolor{blue}{B} from \textcolor{red}{A}.
[1 mark]
Note: the terminology “B from A” is always used, as opposed to “A to B”.
![measuring bearings example](https://mmerevise.co.uk/app/uploads/2020/09/Bearings-Example1.png)
So, we have our two points and a North line coming off both.
The bearing of \textcolor{blue}{B} from \textcolor{red}{A} is measured from the North line going clockwise until we hit the straight line.
Then using a protractor, we measure the angle to be 110\degree which is the bearing of \textcolor{blue}{B} from \textcolor{red}{A}.
Example 2: Drawing Bearings
Two boats \textcolor{red}{A} and \textcolor{blue}{B} are 5km apart, and the bearing of \textcolor{blue}{B} from \textcolor{red}{A} is 256\degree.
Using the scale 1\text{ cm}:1\text{ km}, construct a diagram showing the relative positions of points \textcolor{red}{A} and \textcolor{blue}{B}.
[2 marks]
First, we draw point \textcolor{red}{A} with a North line and measure an angle of 104\degree going anticlockwise from it (This is because 360 - 254 = 104\degree. You can’t measure 256\degree using a protractor any other way).
![draw bearings example](https://mmerevise.co.uk/app/uploads/2020/09/Bearings-Example2-1.png)
Then, as \textcolor{red}{A} and \textcolor{blue}{B} are 5 km apart, we will need to make the line from \textcolor{red}{A} to \textcolor{blue}{B} (going along the bearing we’ve determined) 5 cm long.
The result of this is below, not drawn accurately.
![drawing bearings example](https://mmerevise.co.uk/app/uploads/2020/09/Bearings-Example2-2.png)
Example 3: Finding Bearings
The diagram below shows the bearing of \textcolor{blue}{B} from \textcolor{red}{A}.
Find the bearing of \textcolor{red}{A} from \textcolor{blue}{B}.
![find bearings example](https://mmerevise.co.uk/app/uploads/2020/09/Bearings-Example3-1.png)
[2 marks]
Now, we can’t measure the angle because the diagram is not drawn accurately.
We will use the fact that both North lines are parallel and extend the line \textcolor{red}{A}\textcolor{blue}{B} past point \textcolor{blue}{B}, the angle formed by the North line at \textcolor{blue}{B} and the extension to line \textcolor{red}{A}\textcolor{blue}{B} and the bearing of \textcolor{blue}{B} from \textcolor{red}{A} are corresponding angles (also known as an “F angle”).
So, from our knowledge of parallel lines, we know that they must be equal.
![finding bearings example](https://mmerevise.co.uk/app/uploads/2020/09/Bearings-Example3-2.png)
Finally, we are measuring the line of \textcolor{red}{A} from \textcolor{blue}{B} so we need to go clockwise from the north line at \textcolor{blue}{B} to the line \textcolor{red}{A}\textcolor{blue}{B}.
We have 94\degree but need the remaining portion of the angle.
Fortunately, the remaining portion of the angle is just a straight line, so the bearing of \textcolor{red}{A} from \textcolor{blue}{B} is
94 + 180 = 274\degree
Bearings Example Questions
Question 1: A boat and a lighthouse are 70 miles apart. The bearing of the lighthouse from the boat is 051\degree.
Using the scale 1 cm : 10 miles, construct a diagram showing the relative positions of the lighthouse and the boat.
[2 marks]
Let the lighthouse be L and the boat be B. As we’re finding the bearing of L from B, we shall measure an angle of 051\degree clockwise at B.
Then, as B and L are 70 miles apart, we will need to make the line from B to L 7cm long. The final diagram should look like,
Question 2: The diagram below shows the bearing of A from B. Find the bearing of B from A.
[2 marks]
We can find the other angle around the point B by subtracting 295 from 360,
360\degree - 295\degree = 65 \degree
Then, because the two North lines are parallel, we can say that the bearing of B from A and the 65\degree angle we just found are co-interior. These two angles (marked with red below) must add to 180.
So, we get:
\text{Bearing of B from A } = 180\degree - 65\degree = 115\degree
Question 3: The location C is on a bearing of 140 \degree from A. The bearing of C from B is 250 \degree. Find the location C and mark it on the diagram below.
[2 marks]
Drawing straight lines along each of the bearings, we can find C at the point of intersection of both lines.
Question 4: By measuring the diagram given, state the bearing of B from A.
[1 mark]
By use of a protractor or otherwise we find the angle of 60 degrees. This written as a bearing is,
060 \degree
Question 5: A diagram of a bearing is shown below. Given that the bearing of B from A is 060 \degree, state the bearing of A from B.
[3 marks]
The two North lines are parallel, so we can say that the bearing of B from A and the co-interior angle at B must add to 180 degrees. Thus the co-interior angle is
180 \degree-60\degree = 120 \degree
As angles around a point sum to 360 degrees we can find the bearing of A from B as,
360 \degree-120 \degree=240 \degree
Bearings Worksheet and Example Questions
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Level 4-5GCSENewOfficial MMEBearings Drill Questions
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Bearings - Drill Questions
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