A ladder is placed 6 ft aainsgt a 25 ft building. How high above the ground does the ladder touch the wall?
Is the base of the ladder 6 feet from the building? How tall is the ladder?
To determine the height above the ground where the ladder touches the wall, we can use 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 other two sides.
In this case, the ladder acts as the hypotenuse of the right triangle, and the distance between the base of the ladder and the wall is one side of the triangle. The height above the ground where the ladder touches the wall is the other side of the triangle.
Let's call the distance between the base of the ladder and the wall "a," and the height above the ground where the ladder touches the wall "b." The length of the ladder is the hypotenuse, which we'll call "c."
According to the Pythagorean theorem, we have the equation:
a^2 + b^2 = c^2
Given that the ladder is placed 6 feet against a 25-foot building, we have:
a = 6 ft
c = 25 ft
Substituting these values into the equation, we have:
6^2 + b^2 = 25^2
36 + b^2 = 625
To find b, we need to solve for it. Let's subtract 36 from both sides:
b^2 = 625 - 36
b^2 = 589
Now, we can take the square root of both sides to find b:
b ≈ √589
b ≈ 24.28 ft
Therefore, the ladder touches the wall at a height of approximately 24.28 feet above the ground.