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 away from the house is the base of the ladder?

Answer 1

To find the distance between the base of the ladder and the house, we can use the Pythagorean theorem.

Let's assume the distance from the base of the ladder to the house is 'x' feet.

According to the Pythagorean theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.

In this case, one leg represents the vertical height of the house (12 feet) and the other leg represents the distance from the base of the ladder to the house ('x' feet). The hypotenuse represents the length of the ladder (20 feet).

So, the equation would be: x^2 + 12^2 = 20^2.

Simplifying the equation: x^2 + 144 = 400.

Rearranging the equation: x^2 = 400 - 144.

x^2 = 256.

Taking the square root of both sides: x = 16.

Therefore, the base of the ladder is 16 feet away from the house.