the bottom of a 25 foot ladder is placed 7 feet from a wall. how far up the wall will the ladder reach?
7^2 + h^2 = 25^2
49 + h^2 = 625
h^2 = 576
h = 24
To find how far up the wall the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem 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 forms a right triangle with the wall and the ground. The ladder is the hypotenuse, and we know the lengths of the other two sides.
Given:
Length of the ladder (hypotenuse) = 25 feet
Distance between the ladder and the wall (one side) = 7 feet
Let's call the distance up the wall that the ladder reaches "x."
We can set up the equation using the Pythagorean theorem:
25^2 = 7^2 + x^2
Simplifying, we have:
625 = 49 + x^2
Subtracting 49 from both sides:
576 = x^2
Taking the square root of both sides:
√576 = √x^2
24 = x
So, the ladder will reach a height of 24 feet up the wall.