A ladder 5.5m long is leaning against a wall. the foot of the ladder is 1.7m away from the wall. how far up the wall does the ladder reach?

This is a classic GCSE Pythagoras' Theorem question. 

The first thing we are going to do is draw a diagram. Once we sketch out a diagram, we can see that the ladder makes a triangle shape with the wall. If we insert the numbers that the question provides, we can see that there is one number missing. 

Pythagoras' Theorem says a² + b² = c² with 'c' being the hypotenuse (the longest side) of the right-angled triangle. 

We know that the hypotenuse, 'c' is 5.5 and one of the sides, let's say 'b' is 1.7m. Therefore, we are trying to find 'a'. Lets rearrange by subtracting b² from both sides to make it a² = c² - b² . substitute in the figures and we end up with 

a² = 5.5² - 1.7². If we enter that into a calculator, we get 

a² = 30.25 - 2.89

a² = 27.36

to work out 'a', we just need to take the square root of this number, which is 5.23.