A ladder 6·8m long is leaning against a wall. The foot of the ladder is 1·5m from the wall. Calculate the distance the ladder reaches up the wall.

We have a right angle triangle in this problem. We can use Pythagoras' theorem - the square of the hypotenuse is equal to the sum of the squares of the other two sides of the right angle triangle. We will denote the distance the ladder reaches up the wall as 'h'. Therefore:

1.5² + h² = 6.8² ;

h² = 6.8² - 1.5² ;

h = (6.8² - 1.5²)^0.5 ;

h = 6.6m