a 12ft ladder leans against the side of a house . the bottom of the ladder is 8ft from the side of the house how high is the top of the ladder from the ground round your answer to the nearest tenth
To solve this problem, 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 forms the hypotenuse of the right triangle, and the distance from the bottom of the ladder to the house forms one of the legs. The height from the ground to the top of the ladder forms the other leg.
Let's denote the height from the ground to the top of the ladder as "h". According to the problem, we know the distance from the bottom of the ladder to the house is 8ft and the length of the ladder is 12ft.
Using the Pythagorean Theorem, we have:
h^2 + 8^2 = 12^2
Simplifying the equation:
h^2 + 64 = 144
h^2 = 144 - 64
h^2 = 80
Taking the square root of both sides to solve for h:
h = √80
h ≈ 8.9
Therefore, the top of the ladder is approximately 8.9ft from the ground.