The top of a 12 foot long ladder is leaning against a wall with the top of the ladder 8 feet above the ground.The bottom of the ladder will be _______ feet from the base of the wall
pythagorean theorem!!
x^2 (leg 1) + y^2 (leg 2) = z^2 (hypotenuse = the ladder)
x^2 = (12)^2 - (8)^2
x^2 = 80
x = sq root (80) ~ 8.944
To find the distance in feet from the base of the wall to the bottom of the ladder, we can use the Pythagorean theorem.
The Pythagorean theorem 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 our scenario, the ladder is the hypotenuse, and the height of the wall is one side, while the distance from the base of the wall to the bottom of the ladder is the other side we need to find.
Let's denote the distance from the base of the wall to the bottom of the ladder as "x."
Now, we can set up the equation:
x^2 + 8^2 = 12^2
Simplifying this equation:
x^2 + 64 = 144
Now, we can solve for x by isolating it:
x^2 = 144 - 64
x^2 = 80
Taking the square root of both sides:
x = √80
x ≈ 8.95
Therefore, the bottom of the ladder will be approximately 8.95 feet from the base of the wall.