To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let the length of the ladder, which is the hypotenuse, be represented by c. The distance from the base of the ladder to the house is 6 ft, which can be represented as one of the legs of the right triangle and will be denoted as a. The other leg of the right triangle, representing the height of the ladder, will be denoted as b.
Since we are given that the ladder is 12 ft long, we have c = 12 ft.
Using the Pythagorean theorem, we have: c^2 = a^2 + b^2.
Substituting the given values, we get: (12)^2 = (6)^2 + b^2.
Simplifying, we have: 144 = 36 + b^2.
To isolate b^2, we subtract 36 from both sides: b^2 = 108.
Taking the square root of both sides, we find: b ≈ √108 ≈ 10.4 ft.
Therefore, to make the 12 ft ladder stable with the bottom of the ladder 6 ft from the base of the house, the ladder would reach a height of approximately 10.4 ft.
Sylvia is replacing a piece of siding on her house to make the 12 ft ladder stable the bottom of the letter needs to be 6 ft from the base of her house applying the Pythagorean theorem and rounding to the nearest tenth hell how will the ladder reach so that you'll be a can replace the side
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