Sylvia is replacing a piece of siding on her house. To make the 12ft ladder stable, the bottom of the ladder needs to be 6ft from the base of her house. Applying the Pythagorean Theorem and rounding to the nearest tenth, how high will the ladder reach so that Sylvia can replace the siding.
180ft
13.4ft
10.4ft
108ft
To solve this problem, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the ladder is the hypotenuse and the distance from the base of the house to the bottom of the ladder is one of the other two sides.
Let's call the height that the ladder reaches "h". Using the Pythagorean Theorem, we have:
(6ft)^2 + h^2 = (12ft)^2
36 + h^2 = 144
h^2 = 108
Solving for h, we find:
h = √108
h ≈ 10.4ft
Therefore, the ladder will reach approximately 10.4ft high so that Sylvia can replace the siding. So the answer is 10.4ft.