If you place a 24-foot ladder against the top of a 22-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foo
t.
By using the Pythagorean theorem, we can find the distance between the bottom of the ladder and the bottom of the building.
a^2 + b^2 = c^2
where a is the height of the building (22 feet), b is the distance between the bottom of the ladder and the bottom of the building (what we want to find), and c is the length of the ladder (24 feet).
Substituting the values into the formula, we have:
22^2 + b^2 = 24^2
484 + b^2 = 576
b^2 = 92
b ≈ 9.6
Therefore, the bottom of the ladder will be approximately 9.6 feet from the bottom of the building. Rounded to the nearest tenth of a foot, this is 9.6 feet.
To find the distance between the bottom of the ladder and the bottom of the building, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides (the vertical distance between the bottom of the ladder and the bottom of the building, and the height of the building itself).
So, in this case, let's denote the distance between the bottom of the ladder and the bottom of the building as 'x'. The ladder itself is 24 feet, and the height of the building is 22 feet.
Using the Pythagorean theorem, we have:
x^2 + 22^2 = 24^2
Simplifying the equation, we get:
x^2 + 484 = 576
Subtracting 484 from both sides of the equation:
x^2 = 576 - 484
x^2 = 92
Taking the square root of both sides, we find:
x = √92
x ≈ 9.6 feet
Therefore, the bottom of the ladder will be approximately 9.6 feet from the bottom of the building. Rounded to the nearest tenth of a foot, it would be 9.6 feet.