A ladder is leaning against a building. The base of the ladder is 8 feet from the wall, and the top of the ladder reaches 6 feet up the wall. How long is the ladder?
This makes a right angle triangle. Pythagoras to the rescue!
a^2 + b^2 = c^2
8^2 + 6^2 = c^2
64 + 36 = c^2
100 = c^2
10 = c
To find the length of the ladder, 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 building and the ground. The base of the ladder is one side of the triangle, and the height of the ladder reaching up the wall is the other side. The ladder itself is the hypotenuse.
We are given that the base of the ladder is 8 feet and the height is 6 feet. Let's call the length of the ladder "L". Using the Pythagorean theorem, we can write the equation:
L^2 = 8^2 + 6^2
Simplifying this equation:
L^2 = 64 + 36
L^2 = 100
To find the length of the ladder, we need to take the square root of both sides:
L = √100
L = 10
Therefore, the length of the ladder is 10 feet.