Sylvia is replacing a piece of siding on her house to make the 12 foot ladder stable. The bottom of the ladder needs to be 6 foot from the base of her house, applying the Pythagorean theorem and rounding to the nearest 10th. How high will the ladder reach so that sophia can replace the siding.
To find the height that the ladder will reach, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length 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 is the hypotenuse of the right triangle, the base of the triangle is the distance from the bottom of the ladder to the base of the house, and the height of the triangle is the height that the ladder will reach.
Let's call the height of the ladder "h". According to the Pythagorean theorem, we have:
h^2 = 12^2 - 6^2
Simplifying the equation, we get:
h^2 = 144 - 36
h^2 = 108
Taking the square root of both sides, we find:
h = √108
Using a calculator, we find that √108 ≈ 10.39.
Therefore, the ladder will reach a height of approximately 10.39 feet.