a ladder 20m long rests against a vertical wall so that the foot of the ladder is 1m from the ground
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Is the ladder suspended in space?
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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 length of the hypotenuse (in this case, the ladder) is equal to the sum of the squares of the other two sides.
In this scenario, the ladder forms the hypotenuse of a right-angled triangle, and the wall and the ground form the other two sides. We know that the foot of the ladder is 1m from the ground, so one side of the triangle is 1m. Let's call this side "a".
The length of the ladder is given as 20m, so the hypotenuse is 20m. Let's call this side "c".
By applying the Pythagorean theorem, we can find the length of the third side, which represents the distance from the top of the ladder to the ground. Let's call this side "b".
The equation can be written as follows: a^2 + b^2 = c^2.
Substituting the known values, we have: 1^2 + b^2 = 20^2.
Simplifying, we get: 1 + b^2 = 400.
Solving for b, we subtract 1 from both sides: b^2 = 399.
To find b, we take the square root of both sides: b ≈ √399.
Using a calculator, we find that b ≈ 19.97.
Therefore, the distance from the top of the ladder to the ground is approximately 19.97m.
an unusual position -- the ladder is not on the ground.
I expect you mean the foot of the ladder is one meter from the wall. I assume you want the height of the top of the ladder. If the height up the wall is h, then
1^2 + h^2 = 20^2