Lesson video

Hi, I'm Miss Davies.

In this lesson today, we are going to be using Pythagoras's theorem to work out the length of the shorter sides of a right-angled triangle.

We know, that Pythagoras's theorem states, a squared plus b squared equals c squared.

The most important thing to remember is that the value of c is always the hypotenuse.

The longest side is opposite the right angle.

It doesn't matter which way around a and b are, because addition is commutative.

In this first example, we're calculating the shorter length.

This one is labelled as a.

The hypotenuse is five centimetres and the other shorter length is four centimetres.

First thing we're going to do, is write down Pythagoras's theorem.

We can then substitute our values into Pythagoras's theorem to have a squared plus four squared equals 5 squared.

four squared is 16 and five squared is 25.

This can now be rewritten as, a squared equals 25 subtract 16.

Or a squared equals nine.

To find the length of a, we need to find the square root of nine, which is three centimetres.

In this next example, we're calculating the shorter length again.

This time it's labelled as b.

The hypotenuse is 13 centimetres and the other shorter side is 12 centimetres.

Firstly, we're going to write down Pythagoras's theorem.

a squared plus b squared equals c squared.

We can then substitute in the values that we already know.

This would give us 12 squared, add b squared equals 13 squared.

12 squared is the same as 12 times 12, which is 144.

And 13 squared is 169.

So we have, 144 add b squared equals 169.

We can then, rewrite that, as b squared equals 169 take away 144.

This is the same as b squared equals 25.

To find the length of b, we need to square root 25.

This gives us five centimetres.

So length b is five centimetres.

In this next example, we're calculating the shorter length again, but it's labelled as b.

The hypotenuse is 47 metres, and the other shorter length is 18 metres.

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

Then we can substitute our values for a and c into this, to give 18 squared add b squared equals 47 squared.

18 squared is 324 and 47 squared is 2,209.

I'm now going to rewrite this as b squared equals 2,209 take away 324.

This is the same as b squared equals 1,885.

To find the length of b we need to find the square root of 1,185, which is 43.

4 metres 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.

For part d, the initial equation is going to be 2x squared equals 100.

So you need to divide both sides by two and then square root them.

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.

Adam needs to square 49 to give an answer of seven centimetres.

Here is a question for you to try.

Make sure, that all lengths are in the same units before you apply Pythagoras's theorem.

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

Here is the answer.

The first step for this question is to convert the two metres to 200 centimetres.

Or, you could have converted 80 centimetres to 0.

8 metres.

This could have given an answer of 1.

83 metres.

Here is some questions for you to try.

I would advise you to draw out diagrams to represent the questions.

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

Here are the answers.

Drawing out diagrams would help with answering these worded questions.

Here is some questions for you to try.

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

Here are the answers.

The base of this triangle is 16.

1 centimetres.

This means the perimeter is 53.

1 centimetres, and the area is 398 centimetres squared.

That's all for this lesson, thanks for watching.