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
180 ft.
180 ft.
10.4 ft.
10.4 ft.
13.4 ft.
13.4 ft.
108 ft.
108 ft.
To find the height of the ladder, we can 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 other two sides.
In this case, the ladder acts as the hypotenuse, and the distance from the base of the ladder to the house acts as one side, while the height we're trying to find acts as the other side.
Using the Pythagorean theorem:
c^2 = a^2 + b^2
Where c is the length of the ladder (12 ft), a is the distance from the base of the ladder to the house (6 ft), and b is the height we're trying to find.
12^2 = 6^2 + b^2
144 = 36 + b^2
b^2 = 144 - 36
b^2 = 108
Taking the square root of both sides, we find:
b = √108
Rounding to the nearest tenth, we find that the ladder will reach approximately 10.4 ft. Therefore, the correct answer is 10.4 ft.
To solve this problem, we can use the Pythagorean theorem, which states that 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 (hypotenuse) is 12 ft long and the distance from the base of the ladder to the wall (one of the other sides) is 6 ft. To find the height of the ladder (the other side), we can use the formula:
height^2 = hypotenuse^2 - base^2
height^2 = 12^2 - 6^2
height^2 = 144 - 36
height^2 = 108
Taking the square root of both sides, we find:
height = √108
Rounding to the nearest tenth, we get:
height ≈ 10.4 ft.
Therefore, the ladder will reach a height of approximately 10.4 ft so that Sylvia can replace the siding.
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 (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder forms a right triangle with the ground and the wall of Sylvia's house. The bottom of the ladder is 6 ft. from the base of the house, and the ladder itself has a length of 12 ft.
Let's label the height of the ladder as 'x'. According to the Pythagorean Theorem, we can write the equation:
x^2 = 12^2 - 6^2
Simplifying the equation, we get:
x^2 = 144 - 36
x^2 = 108
Taking the square root of both sides, we find:
x = √108
Rounding to the nearest tenth, we get:
x ≈ 10.4 ft.
So the ladder will reach a height of approximately 10.4 ft. in order for Sylvia to replace the siding on her house.