A ladder which is 10 m long is placed against the wall and reaches a height of 9 m from the ground. How far from the wall is the foot of the ladder? Give non-exact numerical answers correct to 3 significant figures.

This problem can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Here, the ladder acts as the hypotenuse, the wall as one side of the triangle, and the ground as the other side.

We know the length of the ladder (hypotenuse) is 10 m and the height it reaches on the wall is 9 m. We need to find the distance from the wall to the foot of the ladder (the length of the other side).

Let's denote:

• c as the length of the hypotenuse (ladder) = 10 m
• a as the height on the wall = 9 m
• b as the distance from the wall to the foot of the ladder (which we are trying to find)

According to the Pythagorean theorem:

c² = a² + b²

We can rearrange this to solve for b:

b² = c² - a²

Substituting the known values:

b² = 10² - 9² = 100 - 81 = 19

To find b, we take the square root of 19:

b = √19 ≈ 4.36 m

So, the foot of the ladder is approximately 4.36 m from the wall, to three significant figures.