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

Answer 1

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.