Solve Multi-step Problems in Right-Angled Triangles Using Pythagoras' Theorem

In this activity, we are going to use Pythagoras' Theorem to solve multiple-step problems with right-angled triangles. 

You will need a calculator for this activity.

The formula!

In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

  a² + b² = c²

Let's have a look at a multiple-step problem!

Example

Calculate the side k

Answer

We will need to use the top triangle to find a first.

We can then use the answer to find k.

Using Pythagoras' Theorem:

a² =  c² - b²

a² = 12² - 7.3² 

a² = 144 - 53.29 = 90.71

a = √90.71

a = 9.5 cm (1 dp)

We now use this to find k.

a² =  c² - b²

k² = 9.5² - 3.5² 

k² = 90.25 - 12.25

k = √78

k = 8.8 cm (1 dp)

Let's have a go at some more questions like this!