you are cleaning the gutters out of your house which stands 12 feet tall. you are using a ladder that is 20 feet long to reach the gutters. How far from the house is the base of the ladder
To find the distance from the house to the base of the ladder, we can use the Pythagorean theorem.
The ladder forms a right-angled triangle with the ground, the wall (representing the height of the house), and the ladder itself (representing the hypotenuse).
Let x be the distance from the house to the base of the ladder.
According to the Pythagorean theorem, the length of the hypotenuse squared (20^2) is equal to the sum of the squares of the other two sides. In this case, we have:
x^2 + 12^2 = 20^2
Simplifying the equation:
x^2 + 144 = 400
Subtracting 144 from both sides:
x^2 = 256
Taking the square root of both sides:
x = 16
Therefore, the base of the ladder is located 16 feet away from the house.