A ladder 6.2m long is leaning against a wall. The bottom of the ladder is 0.8m from the wall. Calculate the distance the ladder reaches up the wall, giving your answer to two decimal points.

Using the information given, we can draw a diagram of the ladder leaning against the wall. As the wall is at 90 degrees to the ground, we can see that the ladder, wall and ground form a right-angled triangle. The ladder is opposite the right angle and is therefore the hypotenuse of the triangle. Pythagoras' theorem states that a²+b²=c², where a, b and c are the lengths of the sides (with c being the hypotenuse). In this case, we know that a=0.8 (the distance between the wall and the bottom of the ladder) and c=6.2 (the length of the ladder), so we are looking for length b (how far the ladder reaches up the wall). By inputting these numbers into Pythagoras, we get: 0.8²+b²=6.2² By rearranging the equation, we get: b²=6.2²-0.8² b=√(6.2²-0.8²) Using a calculator, we can find out that b=6.14817046. The question asks for our answer to two decimal points, so our final answer is 6.15m.