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 Pythagorean Theorem and rounding to the nearest tenth, how high will the ladder reach so that Sylvia can replace the siding?(1 point)
Responses
108 ft.
108 ft.
10.4 ft.
10.4 ft.
180 ft.
180 ft.
13.4 ft.
To find the height the ladder will reach, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (in this case, the length of the ladder) is equal to the sum of the squares of the other two sides.
Let x be the height the ladder will reach.
Using the Pythagorean Theorem, we have:
x^2 = 12^2 - 6^2
x^2 = 144 - 36
x^2 = 108
Taking the square root of both sides, we get:
x ≈ √108
x ≈ 10.4 ft.
Therefore, the ladder will reach a height of approximately 10.4 ft.