a ladder is leaning againt the side of a building. The ladder is 10 feet away from the building and touches the building at a point 24 feet above the base. How long is the ladder?
a^2 + b^2 = c^2
10^2 + 24^2 = c^2
100 + 576 = c^2
676 = c^2
26 = c
To find the length of the ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this scenario, the ladder, the building, and the ground form a right triangle. The distance between the base of the ladder and the building is one side of the triangle, and the height from the base to where the ladder touches the building is the other side. The ladder itself is the hypotenuse.
Let's denote the length of the ladder as 'L'. The distance between the base of the ladder and the building is given as 10 feet, and the height from the base to the point where the ladder touches the building is given as 24 feet.
Using the Pythagorean theorem, we can set up the equation as follows:
L^2 = 10^2 + 24^2
L^2 = 100 + 576
L^2 = 676
Taking the square root of both sides gives us:
L = √676
L = 26 feet
Therefore, the length of the ladder is 26 feet.