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?
9.8
recall the Pythagorean Theorem:
2^2 + h^2 = 10^2
To determine how far up the building the ladder falls, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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 scenario, the ladder represents the hypotenuse, and the distance from the base of the building to the base of the ladder represents one of the other two sides. Let's call this distance 'x'. The length of the ladder represents the hypotenuse, which is given as 10 feet.
Using the Pythagorean theorem, we can set up the following equation:
x^2 + 2^2 = 10^2
Simplifying this equation, we have:
x^2 + 4 = 100
x^2 = 96
To find the value of x, we can take the square root of both sides:
x = sqrt(96)
This simplifies to:
x ≈ 9.8 feet
Therefore, the ladder falls approximately 9.8 feet up the building.