Use Pythagoras' Theorem to Find a Shorter Side of a Right-angled Triangle

In this activity, we will use Pythagoras' Theorem to find one of the shorter sides!

 

 

Up to now we have only found the longest side - the hypotenuse!

We can use the same formula to find one of the other sides as long as we know the hypotenuse and one other side. 

 

Remember, the squares of the two shorter sides added  is the same as the square of the hypotenuse.

 

 

  a² + b² = c²

 

If we wanted to find a² or b² we just need to rearrange this formula:

a² = c²  -  b²

or

b² = c²  -  a²

 

Let's use this to find a shorter side!

 

Example

Use Pythagoras' Theorem to calculate the length of the shorter side a, in the following right-angled triangle.  

 

 

Answer

By Pythagoras' Theorem:

a² + b² = c²

 

Rearrange first:

a² = c^{2 -} b²

a² = 5² - 4²

a² = 25 - 16

a² = 9

a = √9

c = 3 cm

 

To check: We are finding a shorter side,  so the answer should be smaller than the hypotenuse!

 

 

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