A ladder 20m long rest aganist a vertical wall so that the foot of the ladder is 9m from the wall.

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To solve this problem, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the ladder forms the hypotenuse of a right-angled triangle, with the wall forming one of the other sides, and the distance between the foot of the ladder and the wall forming the remaining side. Let's call the distance between the foot of the ladder and the wall "x".

Applying the Pythagorean theorem, we have:

x^2 + 9^2 = 20^2

Simplifying this equation, we get:

x^2 + 81 = 400

Subtracting 81 from both sides, we have:

x^2 = 319

Taking the square root of both sides, we find:

x ≈ √319

So the distance between the foot of the ladder and the wall is approximately equal to the square root of 319.

If you want a more precise value, you can use the square root function on a calculator or use an online calculator.