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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To find the height at which the top of the ladder will be against the house, we can use the Pythagorean theorem.
The Pythagorean 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, the ground forms one side, and the height we're trying to find forms the other side.
Let's label the sides:
- The length of the ladder (hypotenuse) = 13 feet
- The distance from the base of the ladder to the house (one side) = 5 feet
- The height we're trying to find (other side) = ?
Using the Pythagorean theorem, we can solve for the height:
13^2 = 5^2 + height^2
169 = 25 + height^2
height^2 = 144
To find the height, we take the square root of both sides:
height = √144
height = 12 feet
Therefore, the top of the ladder will be 12 feet above the ground when it rests against the house.