Question

At the start of the day, a painter rested a 3m ladder against a vertical wall so that

the foot of the ladder was 50cm away from the base of the wall.
During the day, the ladder slipped down the wall, causing the foot of the ladder to
move 70cm 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 1 cm.

Answer 1

The ladder slipped down the wall by 70cm. To find this, we can use trigonometry to calculate the initial height of the ladder and the new height of the ladder after it slipped. Subtracting the initial height from the new height gives us the distance the ladder slipped down the wall.

Step-by-step explanation:

The ladder slipped down the wall by 70cm.

To find this, we can use trigonometry. Initially, the ladder forms a right triangle with the wall and the ground, with the distance between the foot of the ladder and the base of the wall as the base of the triangle. The length of the ladder is the hypotenuse. Using the Pythagorean theorem, we can calculate the initial height of the ladder on the wall.

Then, after the ladder slipped, we have a similar right triangle, but with a longer base. We can again use the Pythagorean theorem to find the new height of the ladder on the wall.

Subtracting the initial height from the new height gives us the distance the ladder slipped down the wall, which is 70cm.