Lesson video

Hi everyone, my name is Ms. Coe and I'm really happy to be joining you today because today we're looking at bearings, a great topic as there are so many real life applications.

Let's make a start.

I hope you enjoy the lesson.

Hi everyone, and welcome to this lesson on reverse bearings, under the unit bearings.

And by the end of the lesson you'll be able to work out the bearing of a point A from point B given the bearing of point B from point A.

Today's lesson will consist of lots of key words, so let's look at the first key word, a transversal and a transversal is a line, line segment or ray that intersects through two or more lines at different or distinct points.

We'll also be looking at the keywords corresponding angles and corresponding angles are a pair of angles at different vertices on the same side of a transversal in equivalent positions.

We'll also be looking at alternate angles and alternate angles are a pair of angles, both between or both outside two line segments that are on opposite sides of the transversal that cuts them.

Co-interior angles are on the same side of the transversal line and in between the two other lines.

Today's lesson will also be looking at the word bearing, and a bearing is an angle measured in degrees from north in the clockwise direction and written in three figures.

For example, an angle of 82 degrees is written and said as 082 degrees.

Today's lesson will be broken into two parts.

Firstly, we'll be looking at reverse bearings and then we'll be looking at problem solving with reverse bearings.

So let's make a start looking at reverse bearings.

Knowing all north indicators are parallel because north is in the same direction, allows us to use a range of angle facts to work out bearings.

Here we have four towns that have been plotted on a map and they all sit on the same line segment.

The bearing from A to B is 123 degrees.

What do you think the bearing from B to C is and what do you think the bearing from C to D is? So you can give it a go and explain.

Well done.

Well, they are all 123 degrees.

Now this is because there are corresponding angles as the line is transversal and all the north indicators are parallel.

We can use a range of angle facts associated with parallel lines.

For example, here's a diagram showing two places X and Y.

So what is the bearing from X to Y? Have a little look.

Well, the bearing from X to Y is 120 degrees.

So how do you think we can find the bearing from Y to X? Well, we use our knowledge of co-interior angles.

We know co-interior angles on parallel lines sum to 180 degrees.

Therefore this angle must be 60 degrees.

So now look at the diagram.

How can we find the bearing from Y to X? Have a little think.

Well angles around a point sum to 360 degrees.

So therefore we know the bearing from Y to X is found by 360 degrees subtract 60 degrees gives us a bearing of 300 degrees.

Well done great work.

So let's have a look at your first check.

For each of the diagrams, work out the bearing from A to B and work out the bearing from B to A.

Remember the diagrams aren't drawn accurately.

And press pause as you'll need more time.

Well done.

Let's see how you got on.

Well, let's identify that bearing from A to B.

It's 100 degrees.

Next, we know this angle is 80 degrees because of our knowledge of co-interior angles, so therefore we can work out the bearing from B to A to be 360 degrees, subtract 80 degrees, giving us a bearing of 280 degrees.

Next, let's have a look at that bearing from A to B, it's 043 degrees.

Once again using our knowledge of co-interior angles, we know this is an angle of 137 degrees, so how do we find that bearing from B to A? Well it's 360 degrees subtract 137 degrees giving us a bearing of 223 degrees.

Lastly, we can work out the bearing from A to B to be 119 degrees because of our knowledge of co-interior angles, then we can work out the bearing from B to A to be 299 degrees because of our knowledge of angles around a point sum to 360 degrees.

Well done if you've got this.

Great work.

Let's move on to a slightly harder check, here we have a diagram not drawn accurately and have identified some angles.

What I want you to do is work out the bearing from B to A and then work out the bearing from C to B.

See if you can give it a go.

Press pause if you need more time.

Well done.

Let's see how you got on.

Well, I'm identifying that the co-interior angle here to be 113 degrees.

Therefore this is the bearing I need to find, the bearing from B to A.

So it's simply 360 degrees subtract 113 degrees given me a bearing of 247 degrees.

Well done if you got this.

For part B we're asked to work out the bearing from C to B.

Well to work out this bearing, let's identify this angle using our knowledge of angles around a point sum to 360 degrees.

It's 74 degrees.

Using our knowledge of co-interior angles I know this is 160 degrees.

Now I can work out the bearing from C to B.

The bearing from C to B is found by 360 degrees, subtract 160 degrees, giving me a bearing of 254 degrees.

Well done.

Great work everybody.

So now it's time for your task.

For each of the unscaled diagrams, I want you to work out the bearing from A to B and then I want you to work out the bearing from B to A.

Remember the diagrams are not drawn accurately and I've labelled some angles to help.

See if you can give it a go.

Press pause if you need more time.

Well done.

Let's move on to question two.

Question 2A wants you to work out the bearing of X from W.

B wants you to work out the bearing of Y from X.

C wants you to work out the bearing of W from X and D wants you to work out the bearing of X from Y.

Notice I put some angles in there to help use your knowledge of co-interior angles and angles around a point sum to 360 degrees to help you with this question.

See if you can give it a go, press pause as you'll need more time.

Well done.

Let's move on to question three.

We have a school, church, boathouse and lighthouse were plotted on a map.

Just to let you know I've used the initials, so S is school, C is church, B is boathouse, and L is lighthouse.

And using co-interior angles and other angle facts work out the bearing from S to C, from C to S, from C to B, from B to C, from L to B.

See if you can give it a go.

Press pause if you need more time.

Well done.

Let's see how you got on.

Well for question 1A, the bearing from A to B is 070 degrees, well done.

Hopefully you've worked out that co-interior angle to be 110 degrees.

That means it should have helped you work out that bearing from B to A to be 250 degrees.

Well done.

Next using your knowledge of co-interior angles, we know this angle is 48 degrees and from here it's gonna help us work out the answer to part B, but the answer to part A, the bearing from A to B is 132 degrees and the bearing from B to A is 312 degrees.

Well done if you've got this.

And the last question.

Great question.

Using your knowledge of angles around a point and co-interior angles, the bearing from A to B is 061 degrees and the bearing from B to A is 241 degrees.

Well done, great work.

Let's move on to question two.

Well and identifying all my angles using my knowledge on co-interior angles and angles around a point.

From here I can identify the bearing of X from W to be 053 degrees.

I can work at the bearing of Y from X to be 129 degrees.

I can work at the bearing of W from X to be 233 degrees and it can work out the bearing of X from Y to be 309 degrees.

Well done if you got this.

Lastly, let's have a look at question three.

Great question.

Once again, using our knowledge of co-interior angles and angles around a point, I've worked out these angles to help me identify those bearings.

So the bearing from S to C is 070 degrees.

The bearing from C to S is 250 degrees.

The bearing from C to B is 118 degrees.

The bearing from B2C is 298 degrees and the bearing from L to B is 204 degrees.

Well done if you got this.

Great work everybody.

So now it's time for the second part of your lesson problem solving with reverse bearings, even when diagrams are not drawn accurately, they're still a good visual aid.

Therefore, when diagrams are not provided, a sketch can help work out the bearings.

For example, the question states that the bearing from a plane to a helicopter is 030 degrees.

How can we work out the bearing from the helicopter to the plane? Well we can start by drawing a sketch.

It doesn't have to be a work of art.

I've just drawn my plane and my helicopter.

Notice how I've identified the line segment, then I'm identifying the north and then the question stated that the bearing from the plane to the helicopter is 030 degrees so I've labelled it here.

Now we can use our knowledge of co-interior angles.

So I know this angle here must be 150 degrees.

Remember the question wants us to work out the bearing from the helicopter to the plane.

So I've identified it in green here.

How do you think we can work out the bearing from the helicopter to the plane using my sketch? Well we use the sum of angles around a point.

That means we know the bearing from the helicopter to the plane is 360 degrees.

Subtract 150 degrees to give a bearing of 210 degrees.

Well done.

So let's have a look at some check questions.

First of all, the bearing from the lighthouse to the ship is 065 degrees and we're asked to work on the bearing from the ship to the lighthouse.

See if you can give it a sketch.

Don't forget to label your north, identify those unknown angles using your knowledge of co-interior angles or the sum of angles around a point.

See if you can give check A, a go.

Press pause if you need more time.

Well done.

Let's have a look at check B.

The bearing from Oak Town to Acorn Valley is 125 degrees and you're asked to work out the bearing from Acorn Valley to Oak Town.

Give it a go.

Press pause if you need.

Well done.

Let's have a look at C.

The bearing from town A to town B is 311 degrees and we're asked to work on the bearing from B to A.

Great question.

Same again.

Draw a sketch, label your north, use your knowledge of co-interior angles and angles around a point and identify that bearing from B to A.

Give it a go.

Press pause if you need.

Well done.

Let's see how you got on.

Well for A, this is my sketch.

Like I said, it doesn't have to be a work of art but as long as it clearly shows the bearing of 065 degrees from the lighthouse to the ship.

Using our co-interior angles.

We know this angle is 115 degrees and now I can work out the bearing from the ship to the lighthouse.

It's 245 degrees.

Well done if you got this.

For B here's my sketch.

Once again, doesn't have to be a work of art as long as it clearly shows the bearing from Oak Town to Acorn Valley is 125 degrees.

Using our knowledge of co-interior angles, we know this is 55 degrees and now we can work out the bearing from Acorn Valley to Oak Town to be 305 degrees.

Well done.

Next the bearing from town A to town B is 311 degrees.

Now I've drawn my sketch and I've identified that bearing from town A to town B is 311 degrees.

Like I said, it doesn't have to be a work of art but as long as it clearly shows that bearing.

Now using our knowledge of angles around a point and our co-interior angles, we know the bearing from B to A is 131 degrees, well done.

Now let's move on.

W, X and Y are three towns which form a triangle.

Now angle X, W, Y is 46 degrees.

Angle W, X, Y is 122 degrees and the bearing from W to X is 043 degrees and we're asked to work out the bearing from W to Y and the bearing from Y to X.

Well to do this as always, let's label the north as we're working with bearings so you can see them here.

Now let's annotate the diagram with what we know from the question.

We know the angle X, W, Y is 46 degrees, so I've labelled it here.

We know the angle W, X, Y is 122 degrees, so I've labelled it here.

We know the bearing from W to X is 043 degrees, so I've labelled it here.

Now we also know the sum of angles in a triangle is 180 degrees, so that means I can work out this angle here to be 12 degrees.

I also know co-interior angles exist in our diagram, so I know this is a 137 degrees and we also know the sum of angles around a point is 360.

So this angle is 101 degrees.

Once again, let's use our knowledge of co-interior angles and angles around a point again to work out this to be 79 degrees and this to beat 269 degrees.

Now we have enough information to work out the bearing from W to Y.

I've coloured the bearing from W to Y as green and hopefully you can spot it's a bearing of 089 degrees.

Next we need to work out the bearing from Y to X.

Notice how I've shaded it in here.

I want you to look at my diagram.

What do you think the bearing from Y to X is? Have a little think.

Well it's 269 degrees add on 12 degrees to give us a bearing of 281 degrees.

Really well done.

Great work everybody.

So now it's time for your check.

A, B, and C form a triangle.

Angle ACB is 53 degrees angle ABC is 105 degrees and the bearing from A to B is 115 degrees and the bearing from B to C is 040 degrees and we're asked to work out the bearing from A to C and we're asked to work out the bearing from B to A.

See if you can give it a go, label anything you need using your knowledge of bearings and angle facts, press pause as you'll need more time.

Well done.

Let's see how you got on.

Well first things first, identify those norths and let's label what we know.

We know this angle is 53 degrees.

We know this angle is 105 degrees and we know this angle is 115 degrees.

Now notice the question says that the bearing from B to C is 40 degrees.

So if this is 40 degrees and we know the angle A, B, C is 105 degrees, that means I know this angle is 65 degrees.

Next we know this angle here must be 22 degrees because angles in a triangle sum to 180 degrees.

So that means I can work out the bearing from A to C to be 093 degrees.

Now using our knowledge of co-interior angles, I know this is 87 degrees and using our angles around a point.

I think I've labelled enough here to work out some bearings.

So what's the bearing from A to C? Well it's 093 degrees.

And what's the bearing from B to A? I've labelled it here.

Hopefully you can spot it's 295 degrees.

Really well done if you got this.

Great work everybody.

So now it's time for your task.

Question one A says the bearing from a plane to a ship is 083 degrees and you're asked to work on the bearing from the ship to the plane.

For question B, the bearing from Oak City to Acorn Town is 138 degrees and we're asked to work on the bearing from Acorn Town to Oak City.

For C, the bearing from town A to town B is 268 degrees and we're asked to work on the bearing from B to A.

See if you can give it a go.

Press pause if you need more time.

Well done.

Let's have a look at question two.

What a great question.

The Oak pupils made a treasure map and the map is made with isometric paper laid over it where each triangle in our isometric paper is equilateral.

The length of each triangle is one kilometre.

Now you can only traverse along the lines and we're starting at X and you're asked to find the treasure given these instructions.

Point A is on a bearing of 060 degrees for five kilometres from X.

Point B is on a bearing of 300 degrees for four kilometres from A.

Point B is on a bearing of 060 degrees for two kilometres from C.

Point D is two kilometres north from C.

Point D is also on a bearing of 240 degrees for three kilometres from E.

Point E is on a bearing of 120 degrees for four kilometres from F.

Point F is on a bearing of 060 degrees for three kilometres from G.

Point H is on a bearing of 180 degrees for four kilometres from G and the treasure is buried halfway between H and A.

What a lovely question.

Give it a go.

Press pause as you'll need more time.

Well done.

Let's see how you got on.

Well, for question 1A, you should have got a bearing of 263 degrees.

For 1B, a bearing of 318 degrees and for C, a bearing of 088 degrees.

Well done if you got this.

For question two, starting from each position, always remember to label your north.

We're starting at X, so this is where A is.

Moving on to B this is where B is.

Moving on to C, moving on to D, then E, then F, then G, then H.

And remember the treasure is buried halfway between H and A, so the treasure is right here.

Massive well done if you got this.

Great work everybody.

So in summary, knowing all north indicators are parallel because north is in the same direction, allows us to use a range of angle facts to work our bearings.

And when diagrams are not drawn, sometimes a quick sketch can make things easier.

Not all information is given on a diagram.

Sometimes it must be added or deduced.

Well done.

It was great learning with you.