A ladder is 25 ft long. The ladder needs to reach to a window that is 24 ft above the ground. How far away from the building should the bottom of the ladder be placed?
Please show work.
24^2 + b^2 = 25^2
576 + b^2 = 625
b^2 = 625 - 576
b^2 = 49
b = 7 feet
To find the distance the bottom of the ladder should be placed from the building, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's call the distance the bottom of the ladder should be placed from the building "x". We can set up the following equation:
x^2 + 24^2 = 25^2
Simplifying the equation:
x^2 + 576 = 625
Subtracting 576 from both sides:
x^2 = 49
Taking the square root of both sides:
x = √49
x = 7
So, the bottom of the ladder should be placed 7 ft away from the building.
To solve this problem, you 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 represents the hypotenuse, and the distance from the building to the bottom of the ladder represents one of the legs. The vertical distance from the ground to the window represents the other leg.
Let's denote the distance from the building to the bottom of the ladder as x. According to the problem, the ladder is 25 ft long, and the window is 24 ft above the ground.
Using the Pythagorean theorem, we have:
x^2 + 24^2 = 25^2
Simplifying the equation:
x^2 + 576 = 625
Subtracting 576 from both sides:
x^2 = 625 - 576
x^2 = 49
Taking the square root of both sides, we find:
x = √49
x = 7
Therefore, the bottom of the ladder should be placed 7 ft away from the building.