a ladder that is 15 feet long leans against a house.the top of the ladder rests against the house at a height of 12 feet .how far from the building is the base of the ladder?
Use the Pythagorean Theorem.
a^2 + b^2 = c^2
12^2 + b^2 = 15^2
144 + b^2 = 225
b^2 = 81
b = 9
To find the distance from the building to the base of the ladder, we can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this scenario, the ladder acts as the hypotenuse, and the distance from the building to the base of the ladder is one of the other two sides (let's call it x). The height of the ladder where it touches the house is the second side (12 feet).
Using the theorem, we can set up the equation:
x^2 + 12^2 = 15^2
Simplifying the equation:
x^2 + 144 = 225
Subtracting 144 from both sides:
x^2 = 225 - 144
x^2 = 81
Taking the square root of both sides:
x = √81
x = 9
Therefore, the base of the ladder is 9 feet away from the building.