Lesson video

Hi, I'm Miss.

Davies and in this lesson we're going to begin looking at trigonometry and understand and use tangent, sine, and cosine, which are the three trigonometric ratios.

When working with a right angled triangle with a given angle, we're going to label it slightly differently to how we do it with Pythagoras' theorem.

This side is the hypotenuse.

It is the longest side in the right angled triangle and it is opposite the right angle.

This side is labelled opposite, as it is opposite the given angle.

This is the adjacent side, as it is adjacent, or next to the given angle.

Let's have a look at some more examples.

We always know that this is going to be the hypotenuse, as it is opposite the right angle.

Now that we've been given an angle, we can label our opposite and adjacent sides.

Have a go at this one.

This is our hypotenuse, this is our opposite side, and this is our adjacent side.

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 hypotenuse is always opposite the right angle.

The opposite side is always opposite the angle, and the adjacent side is always the other one that is next to the angle.

We have been asked to identify and label a right angled triangle in this trapezium.

It needs to contain the 63 degree angle.

This is our triangle.

I've drawn a perpendicular line from the base to the vertex between the diagonal and the top sides.

This is going to be the hypotenuse, this is the opposite side, and this is the adjacent.

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.

Make sure that your triangle is right angled and that it contains the whole of the angle that is given.

With trigonometry, we have got three trigonometric ratios.

These are tangent, sine, and cosine.

To work with tangent, we can say the tangent of the angle is equal to the opposite length divided by the adjacent length.

With sine, we can say that sine of the angle is equal to the opposite length divided by by the hypotenuse.

And with cosine, we can say the cos of the angle is equal to the adjacent length divided by by the hypotenuse.

The first thing that we're going to do with this example is label the sides.

We can say that the six centimetre length is the opposite side and the 15 centimetres is the hypotenuse.

Because we have got these two lengths, we would work with sine.

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

Because we have got these two lengths, we would be working with tangent.

In our next example, 15 centimetres is the hypotenuse and six centimetres is the adjacent.

Because we have got these two lengths, we're going to be working with cosine.

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.

Check that you've correctly labelled all of your triangles, as well as identified the correct ratio.

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.

In question four, the hypotenuse is always the longest length, but it doesn't have to be a diagonal.

In question five, Amir is trying to find the opposite side.

He doesn't need to use the adjacent one.

The ratio that he should have selected is sine.

That's all for this lesson.

Thanks for watching.