Question

At the start of the day, a decorator rested a 3m ladder against a vertical wall so that the foot of the ladder was 60cm away from the base of the wall.

During the day, the ladder slipped down the wall, causing the foot of the ladder to move 80cm further away from the base of the wall.
How far down the wall, in centimetres, did the ladder slip? Give your answer to the nearest 1cm.

Answer 1

The ladder slipped down the wall by 29cm when it moved an additional 80cm away from the wall.

Step-by-step explanation:

The student asked how far down the wall a 3m ladder slipped when it moved away from the base of the wall by an additional 80cm, after initially being 60cm from the wall.

To find out how far the ladder slipped, we can use the Pythagorean theorem as this scenario forms a right-angled triangle between the ladder, the wall, and the ground.

Firstly, calculate the initial height (h1) of the ladder against the wall using the initial distance of the ladder's foot from the wall (60cm) and the length of the ladder (3m, which is 300cm).

h1 = \(\sqrt{300^2 - 60^2}\) cm = \(\sqrt{90000 - 3600}\) cm = \(\sqrt{86400}\) cm = 294 cm

Now calculate the final height (h2) after the foot of the ladder moved 80cm further away from the wall (making the total distance from the wall 140cm).

h2 = \(\sqrt{300^2 - 140^2}\) cm = \(\sqrt{90000 - 19600}\) cm = \(\sqrt{70400}\) cm = 265 cm

The ladder slipped down the wall by: 294 cm - 265 cm = 29cm (to the nearest centimetre).