In this activity, you will apply Pythagoras' theorem to various situations.

Let's recap the formula:

If we have a triangle with lengths **a**, **b**, and **c**:

Pythagoras' theorem is:

**a ^{2} + b^{2} = c^{2}**

Remember this only works for **right-angled** triangles.

__Example__

To find the **hypotenuse** (longest side) of the triangle:

Step 1: Square both sides:

10² = 100

3² = 9

Step 2: Add them:

100 + 9 = 109

Step 3: Square root:

√109 = 10.44 cm (to 2 decimal places)

To find a **shorter** side length:

Step 1: Square both sides:

9² = 81

7² = 49

Step 2: Subtract them:

81 - 49 = 32

Step 3: Square root:

√32 = 5.66 (to 2 decimal places)

__What if there isn't a triangle drawn for us?__

This activity will focus on questions where you need to either spot a right-angled triangle within a shape, or make one using the information given.

For example:

I leave my house to go to the bus stop.

I walk 20 m due west and then walk another 30 m due north.

If I had taken the direct route how far would I have walked?

**Draw the situation**

We have been told that the person walks 20m west, followed by 30m north. We can put these lines together as shown:

Now, let's join the shape up...

...And you can see a right-angled triangle has been formed! The direct route would be the diagonal (hypotenuse)

So, we use Pythagoras as follows:

20² = 400

30² = 900

400 + 900 = 1300

√1300 = 36.05 m (2 d.p.)

The key point is to always **sketch the situation,** or look to **find a right angled triangle** within a shape.

Have a go at this activity and see if you can use this skill.