Lesson video

Hi everyone, my name is Miss Ku 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 finding a bearing under the unit bearings.

And by the end of the lesson you'll be able to find a bearing between the points on a map or scale plan.

We have quite a few keywords here, so press pause for more time.

Obviously, we'll be looking at the keyword bearing.

A bearing is an angle measured in degrees from north in the clockwise direction and written with three figures.

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

Today's lesson will be broken into two parts.

We'll be looking at bearings and scale diagrams first, and then we'll be looking at bearings and unscaled diagrams. So let's make a start looking at bearings and scaled diagrams. A diver jumps from her boat and is swimming in the vast ocean.

She loses her way and becomes lost.

What technology do you think is used to help guide her back to the boat? Have a little think.

Well, it's GPS, global positioning system and GPS receivers use signals from satellites to determine exact locations on earth.

And this information is based on the north as a reference point.

So chances are you've already used bearings today if you've used any satellite navigation systems or any GPS.

Now we can appreciate how important bearings are as they use the constant reference of the north to navigate where needed.

In this example, the GPS has allowed the diver to navigate back to the boat.

Looking at this diagram, what bearing for the diver to return back to her boat? Have a little think.

Well, it's 065 degrees, well done if you got that.

So a different diver from the boat is lost and his GPS does not work properly.

The diver is stationary and the boat can track where the diver is.

The boat sends another diver to retrieve the lost diver.

So what instruction does the rescue diver need to save the lost diver? Have a little think.

Well, they need the bearing from the boat to the diver.

Looking at the diagram, what bearing does the rescue diver need to save the lost diver? Well, it's a bearing of 115 degrees.

Well done if you spotted this.

We now know it's sometimes important to follow a bearing to find a position or location and sometimes it's important to find the bearing once a position or location is known.

And we'll look at finding the bearing using scale diagrams first, and this will require using a protractor as diagrams will be drawn accurately in other words, to scale.

So here's an accurately scaled diagram and we have two points drawn, A and B.

I've also labelled the north and the question wants us to measure the bearing from A to B.

So where do you think in the question it tells you to use a protractor? Well it tells you to use a protractor using the word measure and the word measure is telling you to use an instrument.

Now which point are we measuring from first A or B? And I want you to explain how you know.

Well, the word from A states that we're starting at A.

So firstly, let's place the middle spot of our protractor on position A.

So I'm just gonna move it here.

So you can see that middle spot of our protractor is now on A.

Now we have our middle spot of our protractor on A, we're gonna rotate the protractor so the north sits at zero.

we have the centre of protractor on A and the north is at zero.

So now we can read the angle in a clockwise direction.

So let's look more closely to be as accurate as we can.

Alex says the bearing is 111 degrees and Sophia says the bearing is 069 degrees.

Who do you think is correct? And I want you to explain why.

Well, Alex is correct because north is at zero.

Now it's time for your check.

Alex and Sophia correctly placed their protractors to measure the bearing from X to Y.

I want you to write the bearing from X to Y from these two questions.

See if you can give it a go.

Press pause for more time.

Well done.

Let's see how you got on.

Well, the bearing from X to Y in our first question is not 064.

And the bearing from X to Y in our second question is 078.

Well done if you got this.

Now Jacob says the bearing from A to B is 064 degrees.

Explain why Jacob is incorrect.

Have a look at this diagram and have a good think.

Well, he's incorrect because this is the bearing from B to A.

So how would we measure the bearing from A to B, given that we know this angle is a reflex angle? Have a think.

Well, the most efficient way is to measure the anti-clockwise angle and subtract this from 360 degrees.

So let's place the protractor so the centre of the protractor is at A, and remember we're measuring from A.

As we're measuring the anti-clockwise angle, we rotate the protractor so the zero is on north and the values increase anti-clockwise.

As you can see here, I'm rotating my protractor.

So now we have the protractor with the middle pointer A, north is at zero and it's positioned so we can read those anti-clockwise angles.

So let's zoom in so we can read the protractor more accurately.

We're asked to measure the bearing from A to B.

So Alex says 360 degrees, subtract 114 degrees, gives the bearing of 246 degrees, but Sophia says the bearing is 360 degrees, subtract 66 degrees to give a bearing of 294 degrees.

Who do you think is right and explain.

Alex.

The reason why it's Alex is because the anti-clockwise angle is 114 degrees as we count up from the zero at north.

Given that bearings use clockwise angle, we subtract the 114 degrees from our 360 degrees to give us a bearing of 246 degrees.

Well done if you got this.

Great work everybody.

So now it's time for your check.

Alex and Sophia correctly place their protractors so to measure the bearing from X to Y.

We need to write the bearing from X to Y.

See if you can give it a go.

Press pause for more time.

Well done.

Let's see how you got on.

Well, the anticlockwise angle should have been 80 degrees, so therefore the bearing from X to Y is 280 degrees.

For the second question, the anticlockwise angle was 103 degrees, so we do 360, subtract 103 degrees to give a bearing of 257 degrees.

Now don't worry if you are a few degrees out, that's absolutely fine.

It's quite difficult to read when it's on the screen.

Great work everybody.

So now it's time for your task.

The projector has been positioned correctly to work out the bearing from A to B and we're asked to identify the bearing from A to B.

See if you can give it a go.

Press pause if you need more time.

Well done.

Let's move on to question two.

The projector has been positioned correctly to work on the bearing from X to Y.

I want you to identify the bearing from X to Y.

See if you can give it a go.

Press pause if you need more time.

Well done.

<v ->Let's move on to question three.

</v> I've taken away the protractors now and now you need to measure the bearing from X to Y.

Give it a go.

Press pause if you need.

Well done.

Let's move on to question four.

Great question.

Here, you have to measure the bearing from W to X, then measure the bearing from X to Y, then measure the bearing from X to W, then measure the bearing from Y to X.

My little hint to you is to draw arrows showing the north.

See if you can give it a go.

Press pause for more time.

Great work.

Let's see how you got on.

Well for question one, we should have had a bearing of 053 degrees.

For the second question, a bearing of 069 degrees.

For question two, the anti-clockwise angle was 70 degrees.

So 360 subtract 70 degrees gives a bearing of 290 degrees.

The second part, the anti-clockwise angle was a 100 degrees.

So therefore 360 subtract a 100 gives us the bearing of 260 degrees.

Well done.

For question three, remember, you're allowed to be a few degrees out, don't worry, it doesn't have to be absolutely exact.

You're allowed to be a few degrees out.

Well done if you got this.

Well done.

Let's have a look at question four.

Well hopefully you've identified those norths.

So let's measure the bearing from W to X.

Using my protractor, I got a bearing of 039.

The bearing from X to Y, using my protractor, I got a bearing of 114 degrees.

The bearing from X to W, well I needed to work out that anticlockwise angle, which was 139 degrees, giving me a bearing from X to W to be 221 degrees.

Next, let's work out the bearing from Y to X.

While the anticlockwise angle I got was 67 degrees, so the bearing was 360, subtract 67 to give me a bearing of 293 degrees.

Really well done if you got this.

And remember, you are allowed to be a few degrees out, so don't worry if you didn't get these exact values.

Great work everybody.

So now it's time for the second part of our lesson, bearings and unscaled diagrams. Here we have three positions and we know the bearing from A to C is 90 degrees and the angle BAC is 40 degrees.

Laura is asked to work out the bearing from A to B.

Laura says I'm going to use my protractor.

So she gets hair protractor out and she says the bearing from A to B is 052 degrees.

I want you to have a look and explain why Laura is incorrect.

Well, Laura is incorrect because it says diagram not drawn accurately.

This means we must calculate and not measure the bearing.

That means we must calculate the answer using our knowledge of angle facts.

So let's work out the bearing from A to B and show our working out.

Firstly, let's label what we know.

We know angle BAC is 40 degrees.

We want to work out the bearing from A to B, so I've indicated it here.

Therefore the bearing from A to B is 90 degrees subtract 40 degrees, which is a bearing of 050 degrees.

Unlike measuring angles, when calculating the angles, the answer must be exact or to the specified degree of accuracy.

Now let's have a look at a check.

Here's a question.

The question says work out the bearing from B to A.

We have some angles labelled.

Jun says easy.

The bearing from B to A is 065 degrees.

Explain why Jun is wrong and work out the correct answer.

Well, Jun has worked out the bearing from A to B, when the question wants the bearing from B to A.

So, what do we need to do? Well, we need to work out this bearing.

We know the anti-clockwise angle from B to A is 115 degrees, therefore the bearing from B to A is 360 degrees subtract 115 degrees to give me a bearing of 245 degrees.

Well done if you spotted this.

Now it's time for another check.

And given the labelled angles, work out the bearing of B from A.

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 the first part, hopefully you realise this is the bearing we need to find.

So we do 360, subtract 146, subtract 85 to give me a bearing of 129 degrees.

For the second question, this is the bearing we need to find.

So therefore, to work out the bearing from A to B, we do 360 degrees, subtract 123 degrees to give me a bearing of 237.

I always like to really annotate on the diagram to show which bearing I need to find.

For more complex questions, we use more angle facts.

And looking at the diagram, what do you notice? Well, all the norths are parallel to each other.

So as a result we can use our knowledge of angles within parallel lines.

Here we have a question and it shows three towns across the world form a straight line segment when connected.

Now the angle from A to B is at a bearing of 121 degrees.

What is the bearing from B to C? And I want you to give a reason for your answer.

Well we know all the north arrows are parallel, so that means we know length AC is traversal.

It's a straight line intersecting A, B, and C.

So the bearing from B to C is 121 degrees because corresponding angles on parallel lines are equal.

Really well done if you got this.

Great work everybody.

So now it's time for your task.

Four towns are plotted on a map, town C is directly south of town B and towns A, B, and D all lie on the same line segment.

Work on the bearing from B to D, give a reason for your answer and for part B, work out the bearing from A to B and give a reason for your answer.

See if you can give it a go.

Press pause if you need more time.

Well, we know the bearing from B to C is 120 degrees and this is because angles forming a straight line sum to 180 degrees.

Well done if you got this.

And for part B, well the bearing from A to B is also 120 degrees because corresponding angles and parallel lines are equal.

Well done if you got this.

Great work everybody.

So now it's time for your task.

Given the labelled angles, work on the bearing of B from A.

Take your time.

Press pause if you need.

Well done.

Let's move on to question two.

Here we have a beach, lighthouse and a ship and some angles are given.

Work of the bearing from the lighthouse to the ship, the lighthouse to the beach and the ship to the lighthouse.

See if you can give it a go.

Press pause if you need more time.

Well done.

Let's have a look at question three.

Great question.

Five fishing ships follow parallel lines to maximise a catch.

We have to work out the bearing from A to D, the bearing from B to E, the bearing from A to B and 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 move on to question four.

Four towns make up a square and D is directly south of B.

Work out the bearing from A to B, from B to C, from A to D and from D to A.

Well done.

Let's go through these answers.

Well for question one, this is the bearing I need to find.

So the bearing is 165 degrees.

For the second question, this is the bearing I need to find so that therefore I subtract 149 degrees from 360 degrees to give me a bearing of 211 degrees.

Well done if you got this.

Next, the bearing from the lighthouse to the ship is simply 102 degrees.

As we know angles around a point sum to 360 degrees.

The bearing of the lighthouse to the beach is 226 degrees and you can see that from the diagram.

And for C, the bearing from the ship to the lighthouse is 282 degrees.

Well done if you got these.

For question five, well these angles are alternate angles so they are equal.

We can find this angle because the sum of angles and the triangles 180 degrees.

This angle here is a corresponding angle, so therefore we can work out the answers to the question.

The bearing from A to D is 086 degrees.

The bearing from B to E is 086 degrees.

The bearing from A to B is 156 degrees and the bearing from B to A is 336 degrees.

Well done if you got this.

Question four is a great question.

First of all, identify your north and remember the interior angle of a square is 90 degrees.

And here are our answers.

Mark them.

Great work.

Fantastic work everybody.

So in summary, when a diagram is drawn accurately, we can find the bearing using a protractor.

When finding a bearing which is reflex, measuring the anti-clockwise angle and subtracting this from 360 degrees is an efficient method.

Given all norths are parallel for unscaled diagrams, bearings can be calculated using knowledge of angles within parallel lines.

Great work everybody.

It was wonderful learning with you.