Lesson video

Hi.

I'm Miss Davies.

In today's lesson, we're going to be looking at using Pythagoras's theorem to find missing length in a right-angled triangle.

If you watched any of the previous Pythagoras lessons, you will have learned what the word hypotenuse means.

Have a think.

Which side in each triangle is the hypotenuse, and what does it mean? The hypotenuse is the longest side in a right-angled triangle.

It's opposite the right angle.

In the first example, 225 is the longest length and it is opposite the right angle.

So it is the hypotenuse.

In the second example, 65 is larger than both 25 and 60.

And again, it sits opposite our right angle.

In the final example, although two is the smallest number, it is the longest length.

As two metres is longer than 120 centimetres and 1,600 millimetres.

So that is the hypotenuse.

In this example, our hypotenuse is 20 centimetres.

This means the length of the missing side is shorter than 20 centimetres.

I'm going to label our missing length as A.

The first thing we need to do when finding a missing side in a right-angled triangle is to write down Pythagoras's theorem.

We know that our hypotenuse is 20, which is our value for C.

So our value for B is 12.

We substitute these values into Pythagoras's theorem, we get A squared plus 12 squared equals 20 squared.

12 squared is 144 and 20 squared is 400.

We can rewrite this as A squared equals 400 subtract 144.

This means that A squared is equal to 256.

To find the length of side A, we need to find the square root of 256, which is 16.

This means that length A is 16 centimetres.

In this next example, the length we're working out is our hypotenuse.

So I'm going to label it as C.

Again, the first thing we're going to do is write down Pythagoras's theorem.

We can then substitute in our values for A and B.

It doesn't matter which way around we label these, as addition is commutative.

I'm going to say that A is 17 and B is 13.

So that means that 17 squared add 13 squared equals C squared.

17 squared is 289 and 13 squared is 169.

These sum to make 458.

To find the length of C, we need to calculate the square root of 458.

This gives us 21.

40093.

I rounded this to three significant figures, which is 21.

4 metres.

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.

Parts A and C use to find the hypotenuse.

For part B and D, you were finding one of the shorter lengths.

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.

For question two, you might have written down the values for A and B the shorter lengths, the other way around, which is fine.

For question three, the most important thing to make sure, is that the length have measured in the same units.

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.

Ashley runs 501.

6 metres in total.

Becky runs 633.

7 metres in total.

This means that Becky runs 132.

1 metres further.

The next question looks at volume.

So let's have a quick recap of this.

To find the volume of a prism, you multiply the area of the cross-section by the depth.

In this prism, the cross-section is a right-angled triangle.

To work out the area of this, we need to do base multiplied by the height and divide by two.

So it will be 12 multiplied by 20 and divided by two.

This is equal to 240 divided by two, or 220 centimetres squared.

To work out the volume, we're going to multiply 120 by 25 if this is our depth.

This gives us an answer of 3000 centimetres cubed.

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.

The width of the triangular prism is 60 centimetres, which means that the volume of it is 30,000 centimetres cubed.

That's all for this lesson.