Lesson video

Hi, I'm Mrs. Dennett.

Have you all got your bearings? Good, because in this lesson, we're going to be using trigonometry to solve bearings problems. You need to have a good understanding of each of these topics before we begin.

So if you need a little revision, just find the lessons on trigonometry and bearings first.

In this question, we're getting some information about a ship.

The ship is sailing 12 kilometres on a bearing of 73 degrees from a point P.

We want to work out how far East of its original position the ship is.

The best thing to do for this type of question is to start by drawing a diagram.

So we start with our point P, and we know that bearings are measured from North.

So we put our North line in to indicate this, and then we measure a bearing of 73 degrees.

And remember, this is just a sketch.

You don't need to get your protractor out and do it really accurately.

We just need a sketch.

So here's an angle of about 73 degrees and we'll label that.

And then we know that the ship sails 12 kilometres.

So let's draw that in 12 kilometres on a bearing of 73 degrees.

And at this point, we now need to transfer our right-angled triangle, because we're trying to find out how far East the ship is travelling.

So we can draw in a horizontal line and put a question mark above that, to see how far East the ship is travelling.

There's our right angle.

And now we can use trigonometry to help us to solve this problem.

So we label our triangle and we're given the hypotenuse, which is 12 kilometres.

And we're trying to find the opposite side, the length of the opposite side.

That's how far East the ship is travelling.

So we're going to use the Sine ratio, because we've got the hypotenuse and we want to find the opposite side.

So we get Sin 73 equals question mark over 12.

Let's rearrange the equation to solve it.

So we do 12 times Sin 73, work that out on your calculator and you get 11.

48 kilometres to two decimal places.

Let's have a look at another question.

So the ship this time sets sail from point P and it sails eight kilometres due North.

So we can put that in our diagram.

And then it sells five kilometres due East to point Q.

So let's draw that in our diagram as well.

And we've got the point Q, and we want to know what is the bearing of Q from P, and that will be this angle here, because remember our bearings are measured from North in a clockwise direction.

So we're trying to find that angle there, which I've labelled with a question mark.

So now we can label our triangle.

We've got a right-angled triangle.

So we know we can use trigonometry and we label the opposite and adjacent sides, because they're the two sides that we're given some information about, and we're trying to find an angle.

So we're going to use the Tan ratio, and we've got the opposite divided by the adjacent, which is five divided by eight.

And we're going to have to use the inverse Tan function to help us to find the angle.

So we work out Tan to the minus one, a five over eight.

And we work out that the angle is 32.

00538, so on degrees.

And if we round that to the nearest whole number, because bearings were always written to three significant figures, we've got the bearing of Q from P is 032 degrees, We should really say zero three two or 32 degrees.

Here's some questions for you to try.

Pause the video to complete the task and restart when you are finished.

Here are the answers.

It's so important to sketch a diagram for these type of questions before you begin them.

Make sure you put all of the key information in the diagram that you're given in the question, including the distances and the angles, and identify the right-angled triangle carefully, before you start to do any calculations.

Here is a final question for you to try.

Pause the video to complete the task and restart the video when you are finished.

Here's the answer.

You need to work out angle BAC, but then write this as a bearing.

So as bearings are measured from North, we need to add on 90 degrees to get a 118.

81 degrees.

Write this answer to three significant figures because bearings are given with three figures, and that will be 119 degrees.

That's all for this lesson.

Remember to take the exit quiz before you leave.

Thank you for watching.