A ladder 65 feet long is leaning against a wall. Its lower end is 25 feet away from the wall how much farther away will t be if the upper end is moved down 8 feet?
65^2 = 25^2 + h^2 => h = 60
and lowering it h = 52
then,
65^2 = (25 + x )^2 + 52^2 => x = 14
Well, if the ladder is 65 feet long and the lower end is 25 feet away from the wall, we can use some math to find out the distance if the upper end is moved down 8 feet.
Now, when the ladder is leaning against the wall, it forms a right triangle with the wall and the ground. The ladder acts as the hypotenuse, and the distance from the wall to the lower end is the base of the triangle.
So, using the Pythagorean theorem, we can find the height of the triangle (which is the distance the ladder is leaning against the wall) by taking the square root of (65^2 - 25^2).
Calculating that, we get the height to be approximately 60.81 feet.
Now, if we move the upper end of the ladder down 8 feet, we will have a new triangle. The height of this new triangle will be 60.81 - 8 = 52.81 feet.
Therefore, the ladder will be approximately 52.81 feet away from the wall if the upper end is moved down 8 feet. But wait, there's more! You also get a free ladder joke:
Why did the ladder bring a camera to the party?
Because it wanted to take a "shelfie" with all its friends!
To determine how much farther away the ladder will be when the upper end is moved down 8 feet, we can use the Pythagorean theorem.
According to the theorem, in a right-angled triangle, the square of the hypotenuse (ladder) is equal to the sum of the squares of the other two sides (horizontal distance and vertical distance).
Let's denote the original vertical distance as 'x' (distance from the top of the ladder to the ground) and the horizontal distance as 'y' (distance from the bottom of the ladder to the wall). We can set up the following equation:
x^2 + y^2 = 65^2
From the given information, we know that y = 25 (distance from the bottom of the ladder to the wall).
Now, let's calculate the original vertical distance (x) using the equation:
x^2 + 25^2 = 65^2
x^2 + 625 = 4225
x^2 = 3600
x = √3600
x = 60 feet
So, the original vertical distance (x) is 60 feet.
Now, let's move the upper end of the ladder down 8 feet. This means the new vertical distance (x') will be x' = 60 - 8 = 52 feet.
Using the Pythagorean theorem again, we can find the new horizontal distance (y'):
x'^2 + y'^2 = 65^2
52^2 + y'^2 = 4225
2704 + y'^2 = 4225
y'^2 = 4225 - 2704
y'^2 = 1521
y' = √1521
y' = 39 feet
Therefore, when the upper end of the ladder is moved down 8 feet, the ladder will be 39 feet farther away from the wall.
To solve this problem, we can use the Pythagorean theorem, which states that in a right 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 a right triangle with the wall. The ladder's length represents the hypotenuse, and the distance from the wall to the lower end of the ladder is one of the other two sides.
Given that the lower end of the ladder is 25 feet away from the wall, we can consider this as one side of the right triangle. Let's call it "a."
We need to find out how much farther away the upper end of the ladder will be when it moves down 8 feet. Let's assume the new distance is "b."
Using the Pythagorean theorem, we can set up the equation:
a^2 + b^2 = c^2
Substituting the known values, we get:
25^2 + b^2 = 65^2
625 + b^2 = 4225
b^2 = 3600
Now, we can solve for b by taking the square root of both sides:
b = √3600
b ≈ 60
Therefore, when the upper end of the ladder moves down 8 feet, it will be approximately 60 feet farther away from the wall.