A 10-foot ladder is leaning against a wall. The base of the ladder is 2 feet from the base of the building. How far up the building does the ladder fall?
a^2 + b^2 = c^2
The hypotenuse is the ladder.
2^2 + b^2 = 10^2
4 + b^2 = 100
b^2 = 96
b = 9.8 feet
To determine how far up the building the ladder falls, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the ladder is the hypotenuse, and the two sides are the distance it touches the ground (2 feet) and the distance it touches the building (unknown). Let's call the distance it touches the building "x".
Therefore, the equation becomes:
2^2 + x^2 = 10^2
Simplifying the equation:
4 + x^2 = 100
Subtracting 4 from both sides:
x^2 = 96
Now, to solve for x, we can take the square root of both sides:
x = √96
Using a calculator, we find that:
x ≈ 9.8 feet
Therefore, the ladder falls approximately 9.8 feet up the building.