ladder 13 feet long . if she set the base of the ladder on the level ground 5 feet from the side of a houes, how many feet above the ground will the top of the ladder be when it rest against the house?

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144ft

To find out how many feet above the ground the top of the ladder will be when it rests against the house, you can use the Pythagorean theorem. The theorem states that in a right-angled 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 the hypotenuse of a right-angled triangle. The base of the ladder on the level ground represents one side of the triangle, and the height from the ground to the top of the ladder represents the other side.

Let's call the height of the ladder "h." According to the problem, the ladder is 13 feet long (the hypotenuse) and is set 5 feet away from the house (the base). Using the Pythagorean theorem, we can set up the equation:

h^2 + 5^2 = 13^2

Simplifying the equation:

h^2 + 25 = 169

Next, we can isolate the h^2 term:

h^2 = 169 - 25

h^2 = 144

Finally, we can take the square root of both sides to solve for h:

h = √144

h = 12

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