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Hi, I'm Miss Davies.

In this lesson we're going to be applying trigonometry to different scenarios.

When we're using trigonometry, we need to make sure that we are correctly labelling the sides.

In any right angled triangle, the length opposite the right angle is the hypotenuse.

With trigonometry, you are always given an angle.

The length that is opposite this angle is the opposite.

The other length is the adjacent, as it is next to the given angle.

In this next example, we're going to start off by labelling the hypotenuse again.

Then the opposite, which is opposite the given angle.

And finally, the side that is adjacent to the given angle.

Let's recap choosing the trigonometric ratio to use.

In this example we have been given six centimetres and 15 centimetres.

The six centimetre side is the opposite.

The 15 centimetre side is the hypotenuse.

Because we have got these two lengths, we're going to work with sine.

In this next example six centimetres is the adjacent, 15 centimetres is the opposite side.

Because these are the two sides that we would be working with, it is tangent.

In this final example, the hypotenuse is 15 centimetres, the adjacent is six centimetres.

Because we have got these two sides, we would work with cosine.

In this example we have been asked to calculate the length of the line segment CD.

In that triangle that is BCD, we don't know any of the lengths.

We need to start off by calculating the length BD.

The first thing we're going to do is label those two sides.

The length AB is the hypotenuse of that triangle and the length BD is the opposite length.

This means that we are going to use sine.

Sine of the angle, which is 58 degrees, is equal to the opposite divided by the hypotenuse.

This is the equation we're going to work with to calculate the length BD.

To calculate BD, the first thing we're going to do is multiply both sides by 6.

4.

This means that BD is equal to 6.

4 multiplied by sine of 58.

We can type into our calculators 6.

4 multiplied by sine 58 to get 5.

4275 as the length BD.

We can then use this to calculate the length CD.

CD is the opposite side and BD, which we've just worked out, is the adjacent side.

This means that we're going to work with tan.

If we substitute in the values that we've been given, this is equal to tan 31 is equal to CD divided by 5.

4275.

We're going to multiply both sides by 5.

4275, then we can type this into our calculator to get the length CD is equal to 2.

08 centimetres to three significant figures.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

The height of this triangle is 6.

062 metres.

We can then use this to find the length BD is 11.

5 metres to one decimal place.

This is an isosceles triangle.

We can only apply trigonometry to right angled triangles.

How can we form a right angled triangle from this isosceles triangle? We can split our isosceles triangle into two congruent right angled triangles.

The hypotenuse of each triangle is 15 centimetres.

What is the base of each triangle going to be? It's going to be nine centimetres, as the total base of the isosceles triangle was 18 centimetres.

In this example we have been asked to calculate the height of the isosceles triangle.

If we split this into two congruent right angled triangles, this is what we would be working with.

We have been asked to calculate the height, which I've labelled as a.

Because we have got two labelled sides and an angle, we're going to be working with trigonometry.

So let's start by labelling our triangle.

The height is the opposite length and 15 centimetres is our hypotenuse.

We will be working with sine.

Sine of 35 is going to be equal to a divided by 15.

To solve this equation for a, we're going to multiply both sides by 15.

We can then type this into our calculator to get a solution of a is equal to 8.

60 centimetres correct to three significant figures.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

The height of this triangle is 13.

7374 centimetres.

To work out the area, you're going to multiply this by 10 and divided by two.

If you've used the Answer button on your calculator, it will give you an answer of 68.

6869.

The correct answer is anywhere between 68.

5 and 68.

7 centimetres squared.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

You should have worked out 25 multiplied by cos 40, which is 19.

2 kilometres to one decimal place.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

The missing lengths of this triangle are 7.

2 metres and 5.

4 metres, both to one decimal place.

This means that the total amount of fence needed is 21.

6 metres.

As the shop only sells the fence in one metre panels, you need 22 metres.

22 multiplied by two pound 16 is going to cost 47 pound 52 in total.

That's all for this lesson.

Thanks for watching.