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)
108
180 n
104 R
O 134 h
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 (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, the ladder represents the hypotenuse of a right triangle, with one side measuring 12 ft (the length of the ladder) and the other side measuring 6 ft (the distance of the ladder's bottom from the base of the house).
Using the Pythagorean Theorem, we can solve for the height (h) as follows:
c^2 = a^2 + b^2
h^2 = 12^2 - 6^2
h^2 = 144 - 36
h^2 = 108
Taking the square root of both sides, we find:
h = √108 ≈ 10.4
Rounding to the nearest tenth, the ladder will reach approximately 10.4 ft high.
Therefore, the correct answer is 104 R.
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 (in this case, the ladder) is equal to the sum of the squares of the other two sides.
Let's denote the height that the ladder will reach as 'h', and the base of the ladder (or the distance from the base of the house) as 'b'.
According to the problem, the bottom of the ladder needs to be 6 ft from the base of her house, so b = 6 ft.
We have a right triangle with the height (h), the base (b), and the hypotenuse (ladder).
Using the Pythagorean Theorem, we can write:
h^2 + b^2 = ladder^2
Substituting the given values into the formula:
h^2 + 6^2 = ladder^2
Simplifying:
h^2 + 36 = ladder^2
To solve for h (the height that the ladder will reach), we need to find ladder^2, which is the square of the hypotenuse.
We know that the ladder length is 12 ft, so ladder^2 = 12^2 = 144.
Substituting this value into the equation:
h^2 + 36 = 144
Subtracting 36 from both sides of the equation:
h^2 = 144 - 36
h^2 = 108
To find the value of h, we can take the square root of both sides:
sqrt(h^2) = sqrt(108)
h = √108
Rounding to the nearest tenth:
h ≈ 10.4 ft
Therefore, the ladder will reach approximately 10.4 feet high so that Sylvia can replace the siding.
To find how high the ladder will reach, we can use the Pythagorean Theorem, which states that in a right triangle, the square 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 sides of the right triangle are the distance from the base of the ladder to the house (6 ft) as the base, and the height the ladder reaches as the other side. The hypotenuse is the length of the ladder.
Let's denote the height the ladder reaches as "h" and the length of the ladder as "c". According to the Pythagorean Theorem:
c^2 = 6^2 + h^2
We are given that the length of the ladder is 12 ft, so c = 12. Substituting this into the equation:
12^2 = 6^2 + h^2
Simplifying:
144 = 36 + h^2
Subtracting 36 from both sides:
h^2 = 144 - 36
h^2 = 108
To find the value of h, we take the square root of both sides:
h = sqrt(108)
Rounding to the nearest tenth:
h ≈ 10.4 ft
Therefore, the ladder will reach a height of approximately 10.4 ft.