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)
• 108 ft.
• 180 ft.
• 13.4 ft.
• 10.4 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, and the distance from the base of the ladder to the house is one of the other sides. We are given that the bottom of the ladder needs to be 6 ft. from the base of the house, so this is the length of one side of the triangle.
Let's denote the height the ladder reaches as 'h'. According to 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, we find:
h = sqrt(108)
Now, rounding to the nearest tenth:
h ≈ 10.4 ft.
Therefore, the ladder will reach approximately 10.4 ft.
To find out how high the ladder will reach, we can use the Pythagorean Theorem. According to the theorem, the square of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides.
Let's assign the length of the ladder to be 'c', the distance from the bottom of the ladder to the base of the house to be 'a', and the height of the ladder to be 'b'.
Given:
a = 6 ft
c = 12 ft
Using the formula of the Pythagorean Theorem:
c^2 = a^2 + b^2
Substituting the given values:
12^2 = 6^2 + b^2
Simplifying:
144 = 36 + b^2
Rearranging the equation:
b^2 = 144 - 36
b^2 = 108
Taking the square root of both sides:
b = √108
Rounding to the nearest tenth:
b ≈ 10.4 ft
Therefore, the correct answer is 10.4 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 forms a right triangle with the ground and the side of Sylvia's house. We can label the height of the house as 'h', the distance from the base of the ladder to the house as '6 ft', and the length of the ladder as '12 ft'.
According to the Pythagorean theorem, we can write the equation:
(6 ft)^2 + h^2 = (12 ft)^2
Simplifying the equation, we have:
36 + h^2 = 144
Now, we can solve for 'h' by subtracting 36 from both sides:
h^2 = 144 - 36
h^2 = 108
To find the value of 'h', we take the square root of both sides:
h ≈ √108
Rounding to the nearest tenth, h is approximately equal to 10.4 ft.
Therefore, the ladder will reach a height of approximately 10.4 ft.
The correct answer choice is:
• 10.4 ft.
Are you sure
Yes, I am sure. Based on the given information and using the Pythagorean theorem, the ladder will reach a height of approximately 10.4 ft. The correct answer choice is 10.4 ft.
An electric pole has a support cable that is attached to the pole 20 ft. from the ground. The cable is anchored on the ground 10 ft. from the base of the pole. How long is the cable? Round to the nearest tenth. (1 point)
• 17.3 ft.
• 22.4 ft.
• 500 ft.
• 300 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 cable forms a right triangle with the ground and the pole. We can label the length of the cable as 'c', the height of the pole as 'a', and the distance from the base of the pole to the anchor point as 'b'.
According to the Pythagorean theorem, we can write the equation:
a^2 + b^2 = c^2
Substituting the given values:
a = 20 ft
b = 10 ft
We can now solve for 'c' by plugging in the values:
(20 ft)^2 + (10 ft)^2 = c^2
Simplifying the equation:
400 ft^2 + 100 ft^2 = c^2
500 ft^2 = c^2
To find the value of 'c', we take the square root of both sides:
c ≈ √500
Rounding to the nearest tenth, c is approximately equal to 22.4 ft.
Therefore, the length of the cable is approximately 22.4 ft.
The correct answer choice is:
• 22.4 ft.
Are you positive
Apologies for the confusion in the previous response. Let's re-assess the problem:
Given:
a = 20 ft (height of the pole)
b = 10 ft (distance from the base of the pole to the anchor point)
We are asked to find the length of the cable, which is represented by the hypotenuse 'c' in the right triangle.
Using the Pythagorean theorem, the equation can be written as:
c^2 = a^2 + b^2
Substituting the given values:
c^2 = 20^2 + 10^2
c^2 = 400 + 100
c^2 = 500
Taking the square root of both sides:
c ≈ √500
Rounding to the nearest tenth:
c ≈ 22.4 ft
Therefore, the length of the cable is approximately 22.4 ft.
The correct answer choice is:
• 22.4 ft.