Larry has a ladder that is 16' long. If he sets the base of the ladder on level ground 5 feet from the side of the house, how many feet above the ground will the top of the ladder reach when it rests against the house?
5^2 + h^2 = 16^2
To find the height that the top of the ladder will reach, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, and the base of the ladder is one side of the right triangle. The height we want to find is the other side of the right triangle.
Given that the ladder is 16 feet long and the base is 5 feet, we can set up the equation:
hypotenuse^2 = base^2 + height^2
16^2 = 5^2 + height^2
Simplifying the equation:
256 = 25 + height^2
Subtracting 25 from both sides:
231 = height^2
Taking the square root of both sides:
sqrt(231) ≈ 15.2
Therefore, the top of the ladder will reach approximately 15.2 feet above the ground when it rests against the house.