Sylvia is replacing a piece of siding on her house. To make the 12ft. ladder stable, the bottom of the ladder needs to be 6ft. 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. 10.4 ft.
2. 108 ft.
3. 13.4 ft.
4. 180 ft.
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 is the hypotenuse, the distance from the base of the house to the bottom of the ladder is one of the sides, and the height Sylvia needs to reach to replace the siding is the other side.
Let's call the height Sylvia needs to reach "h". According to the problem, the distance from the base of the ladder to the bottom of the house is 6ft. The length of the ladder is 12ft.
Using the Pythagorean theorem, we can write the equation as:
6^2 + h^2 = 12^2
Simplifying the equation, we have:
36 + h^2 = 144
Subtracting 36 from both sides, we get:
h^2 = 108
Taking the square root of both sides, we find:
h ≈ 10.4 ft.
Therefore, the ladder will reach approximately 10.4 ft. high so that Sylvia can replace the siding.
Answer: 1. 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 is the hypotenuse, with a length of 12 ft, and the distance from the base of the ladder to the house is 6 ft.
Using the Pythagorean theorem:
c^2 = a^2 + b^2
where c is the length of the hypotenuse (12 ft), and a and b are the lengths of the other two sides (which we want to find).
12^2 = 6^2 + b^2
144 = 36 + b^2
Now, subtracting 36 from both sides:
108 = b^2
Taking the square root of both sides:
b ≈ √108
b ≈ 10.4 ft
Therefore, the ladder will reach a height of approximately 10.4 feet.
So the answer is option 1: 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 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 acts as the hypotenuse, and the distance of the ladder from the base of the house (6ft) acts as one of the other sides. Let's call the height the ladder will reach 'h'.
So, according to the Pythagorean Theorem:
h^2 = 12^2 - 6^2
Simplifying:
h^2 = 144 - 36
h^2 = 108
To find the value of 'h', we can take the square root of both sides:
h = sqrt(108)
Now, let's round the value to the nearest tenth:
h ≈ 10.4 ft.
Therefore, the correct answer is option 1: 10.4 ft.