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
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 length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's represent the height of the ladder as "h". The base of the ladder is 6 ft, and the length of the ladder (the hypotenuse) is 12 ft. Using the Pythagorean theorem, we can write the equation:
6^2 + h^2 = 12^2
36 + h^2 = 144
h^2 = 144 - 36
h^2 = 108
Taking the square root of both sides, we get:
h = √108 ≈ 10.4
Therefore, the ladder will reach a height of approximately 10.4 ft.
To find the height the ladder will reach, we can use the Pythagorean theorem, which states that in a right-angled 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 acts as the hypotenuse.
Let's assume the height the ladder will reach is represented by side b, and the distance from the base of the ladder to the house is represented by side a.
According to the problem, the bottom of the ladder needs to be 6 ft. from the base of Sylvia's house. So, side a = 6 ft.
The length of the ladder is given as 12 ft, which is the hypotenuse, represented by side c.
Using the Pythagorean theorem, we can write the equation as:
c^2 = a^2 + b^2
Substituting the known values, we get:
12^2 = 6^2 + b^2
Simplifying:
144 = 36 + b^2
Subtracting 36 from both sides:
b^2 = 144 - 36
b^2 = 108
Now, to find the value of b, we take the square root of both sides:
b = √108
b ≈ 10.4
Therefore, to the nearest tenth, the ladder will reach a height of approximately 10.4 feet so that Sylvia can replace the siding on her house.
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 length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this scenario, the ladder is the hypotenuse, and the distance from the base of the ladder to the house forms one of the legs of the right triangle. The other leg represents the height the ladder will reach.
Let's denote the height the ladder will reach as "h". We already know that the bottom of the ladder needs to be 6 ft. from the base of the house, which forms one leg of the triangle. The length of the ladder is given as 12 ft., which is the hypotenuse.
Now we can use the Pythagorean Theorem to solve for "h".
Applying the theorem, we have:
h² + 6² = 12²
Simplifying the equation, we get:
h² + 36 = 144
Subtracting 36 from both sides:
h² = 108
To find the value of "h", we take the square root of both sides:
h ≈ √108
Using a calculator, we can approximate the square root of 108 as:
h ≈ 10.39
Rounded to the nearest tenth, the ladder will reach a height of approximately 10.4 ft. so that Sylvia can replace the siding.