Topic outline
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Video transcriptThis unit of work is on Bearings.
Not all learners will have experience of bearings prior to commencing Cambridge IGCSE Mathematics.
And confidence in bearings is sometimes required when learners apply their conceptual understanding of other topics to solve multi-step problems involving bearings.
In this unit learners will develop an understanding of bearings as a practical application of angle as a measure of turn.
Extended students will apply their understanding to sine and cosine rule problems.
This unit of work is just one of several approaches that you could take when teaching this topic and you should aim to adapt the resources to match ability level of your learners as well as your school context.
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Lesson 3 video
Video transcript
Let's consider a bearings problem about the journey of a ship.
A ship sails 22km on a bearing of zero four two degrees from point A, and a further 30km on a bearing of zero nine zero degrees to arrive at point B.
What is the bearing of B from A?
The first thing you need to do with any problem like this is to draw a diagram.
Spend a few moments drawing the diagram yourself.
Here is our diagram for this problem.
To find the bearing of B from A we will need to work out the size of angle alpha.
The triangle that we need to work with to solve this problem is a non-right-angled triangle so this tells us that we are likely to have to use either the sine or cosine rule to help solve this problem.
But at the moment we have very little information about this non-right-angled triangle.
First let's concentrate on finding more information about the right-angled triangle.
Angle theta sits within a right-angled triangle.
We use the fact that the sum of angles in a triangle is 180 degrees to calculate theta as we know the sizes of the other angles.
Spend a few moments working out the size of angle theta yourself.
Theta is 48 degrees.
Let's mark this angle on our diagram.
Now we can find the size of angle beta as both these angles lie on a straight line and angles around a point on a straight line sum to 180 degrees.
Work out the size of angle beta yourself.
Angle beta is 132 degrees.
Having put this information into our diagram. Let's look again.
If we remove all the other information from this diagram we can see that we have a non-right-angled triangle for which we know two sides and the angle between them.
In this situation the cosine rule can be used to find the opposite length AB.
Spend a few moments calculating the length of AB yourself.
AB is 48km to the nearest km.
We now have nearly all the information that we need to calculate the solution to this problem.
We can use our non-right-angled triangle for which we have two sides and an opposite angle.
To find angle alpha we can use a rearrangement of the sine rule.
Spend a few moments calculating the size of angle alpha yourself.
Angle alpha is 28 degrees to the nearest degree.
We haven't quite finished yet and it is very easy to give our final answer as 028 degrees to the nearest degree but we still need to work out the bearing of B from A measured from North.
We must add out new value for alpha to our original bearing 042 degrees.
Don't forget the final bearing needs to be written using 3 figures.
So the bearing of B from A is 070 degrees.
Well done!
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