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. 13.4 ft. 13.4 ft. 10.4 ft. 10.4 ft. 180 ft.
To solve this problem, we need to use the Pythagorean theorem, which 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 lengths of the other two sides.
In this case, the ladder represents the hypotenuse, and the distance from the base of the ladder to the house represents one of the sides. We can label the height of the ladder as "h" and the distance from the base of the ladder to the house as "6ft".
Using the Pythagorean theorem, we can write the equation:
h^2 = 12^2 - 6^2
Simplifying:
h^2 = 144 - 36
h^2 = 108
Taking the square root of both sides:
h = √108
Rounding to the nearest tenth, the height of the ladder will reach approximately 10.4 ft. Therefore, the correct answer is 10.4 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 (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder, the base of the house, and the height of the ladder form a right triangle, with the ladder being the hypotenuse.
Given the ladder is 12 ft. long and the bottom of the ladder is 6 ft. from the base of the house, we can label the base of the triangle as 6 ft., the height of the ladder as "x" ft., and the hypotenuse (the ladder) as 12 ft.
Using the Pythagorean Theorem, we can solve for the height "x":
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 approximately 10.4 ft. in height, rounded to the nearest tenth.
To find the height that the ladder will reach, we can use the Pythagorean Theorem, which states that in a right-angled 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 ladder is the hypotenuse, the height it reaches is one of the sides, and the distance from the house to the ladder is the other side.
Let's denote the height reached by 'h', the distance from the house to the ladder by 'd', and the length of the ladder by 'L'. According to the problem, d is 6 ft and L is 12 ft.
Using the Pythagorean Theorem, we have:
h^2 + d^2 = L^2
Substituting the given values:
h^2 + 6^2 = 12^2
h^2 + 36 = 144
Subtracting 36 from both sides:
h^2 = 108
To find the value of h, we need to take the square root of both sides:
h = √108
Now, rounding to the nearest tenth, we can evaluate this square root:
h ≈ 10.4 ft
Therefore, the ladder will reach approximately 10.4 ft high so that Sylvia can replace the siding.
The correct answer is 10.4 ft.