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.

For answering this question we need to understand Pythagoras theorem. It states that when a triangle has a right angle (90º) the square of the hypotenuse is equal to the sum of the squares of the two other sides. Knowing this, we will establish the 6.8m long side as the hypotenuse (we will call it "c"), the 1.5m long side as one of cathetus (we will cal it "a") and the other cathetus is the unknown (we will call it "b"). Substituting into the equation that the theorem gives us: c^2=b^2+a^2; we get that: b^2= 6.8^2-1.5^2; then b=6.6m.