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 replace the siding?
Using the Pythagorean theorem, we can solve for the height of the ladder. Let the height be denoted as 'h'.
According to the problem, the base of the ladder is 6 ft from the base of the house, the ladder is 12 ft long, and the height of the ladder is 'h'.
Thus, we can form the equation:
6^2 + h^2 = 12^2
Simplifying this equation, we have:
36 + h^2 = 144
Subtracting 36 from both sides, we have:
h^2 = 108
Taking the square root of both sides, we have:
h ≈ √108 ≈ 10.4 ft
Therefore, to the nearest tenth, the ladder will reach a height of approximately 10.4 ft.
To find the height that the ladder will reach, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
Here, the ladder acts as the hypotenuse, and the distance of the bottom of the ladder from the base of the house acts as one of the legs.
The other leg represents the height the ladder will reach, which we need to find.
Let's label the hypotenuse as "c," the length of one leg as "a," and the length of the other leg as "b."
From the given information, we have:
a = 6 ft (distance from the base of the house to the bottom of the ladder)
c = 12 ft (the length of the ladder)
Using the Pythagorean theorem, we have:
a^2 + b^2 = c^2
Substituting the known values, we get:
6^2 + b^2 = 12^2
36 + b^2 = 144
b^2 = 144 - 36
b^2 = 108
To find the value of "b," we take the square root of both sides:
√(b^2) = √(108)
b = √108
Rounding to the nearest tenth, we have b ≈ 10.4 ft.
Therefore, the ladder will reach a height of approximately 10.4 ft.
To find the height that the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem 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 lengths of the other two sides.
In this case, the ladder forms a right triangle with the ground and the height of the wall. The ladder is the hypotenuse, the 6 ft. distance from the base of the house is one of the legs, and we want to find the length of the other leg, which represents the height the ladder will reach.
Using the Pythagorean theorem, we can set up the equation:
length of ladder^2 = 6^2 + height^2
To solve for the height, we need to rearrange the equation:
height^2 = length of ladder^2 - 6^2
Now let's substitute the given values:
height^2 = 12^2 - 6^2
height^2 = 144 - 36
height^2 = 108
To solve for the height, we take the square root of both sides of the equation:
height = sqrt(108)
Using a calculator, we find that the square root of 108 is approximately 10.4.
Rounding to the nearest tenth, the ladder will reach a height of 10.4 ft.