A women has a ladder that is 13 feet long.if she sets the base of the ladder on level ground 5 feet from the side of a house,how many feet above the ground will the top of the ladder be when it rests against the house?

5-12-13 is a common Pythagorean triple

To find the height at which the top of the ladder will rest against the house, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right 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 case, the ladder forms a right triangle with the ground and the side of the house. The ladder itself is the hypotenuse, the distance from the base of the ladder to the house is one side, and the height from the ground to the top of the ladder is the other side we want to find.

Let's denote the height we are looking for as 'h'. According to the Pythagorean theorem, we have:

(5 feet)^2 + h^2 = (13 feet)^2

Simplifying this equation, we get:

25 + h^2 = 169

Subtracting 25 from both sides, we have:

h^2 = 144

Taking the square root of both sides, we get:

h = 12

Therefore, the top of the ladder will be 12 feet above the ground when it rests against the house.