Sylvia is replacing a piece of siding on her house to make the 12-ft ladder stable the bottom of the ladder needs to be 6 ft from the base of her house applying the high score in theorem and rounding to the nearest tenth how high will the ladder reach so Sylvia can replace the siding
The Pythagorean theorem states that in a right 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 is the hypotenuse, and the distance from the bottom of the ladder to the base of the house is one of the other two sides. Let's call this distance x. The height reached by the ladder will be the remaining side, which we will call h.
According to the Pythagorean theorem, we have:
x^2 + h^2 = 12^2
Since we know that x = 6 ft, we can substitute this value into the equation:
6^2 + h^2 = 12^2
36 + h^2 = 144
h^2 = 144 - 36
h^2 = 108
Taking the square root of both sides, we get:
h = sqrt(108)
h ≈ 10.39 ft
Therefore, the ladder will reach a height of approximately 10.39 feet.