Use Pythagoras' Theorem

Pythagoras' Theorem states that:

 

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

 

 

 In other words, the area of the two orange squares fits perfectly into the area of the purple square.

 

 We can write it like this in short:

  a² + b² = c²

 

 

Remember that, the triangle must be right-angled and the hypotenuse is always the longest side and the one opposite the right angle.

 

Let's use this information to find a missing side!

 

Example

Use Pythagoras' Theorem to calculate the length of the hypotenuse, C, in the following right-angled triangle.  

Give your answer to 1 decimal place.

 

 

Answer

By Pythagoras' Theorem:

a² + b² = c²

7² + 5² = c²

c² = 49 + 25

c² = 74

c = √74

c = 8.6 (to 1 decimal place)

 

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