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
108 ft.
108 ft.
13.4 ft.
13.4 ft.
180 ft.
180 ft.
10.4 ft.
To solve this problem, 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.
In this case, the ladder is the hypotenuse, the distance from the base of the house to the bottom of the ladder is one leg, and the height reached by the ladder is the other leg.
Let's represent the height reached by the ladder as 'h'. We can set up the equation:
(6 ft)^2 + h^2 = (12 ft)^2
Simplifying and solving for 'h':
36 ft + h^2 = 144 ft
h^2 = 144 ft - 36 ft
h^2 = 108 ft
Taking the square root of both sides:
h = √108 ft
Rounding to the nearest tenth:
h ≈ 10.4 ft
Therefore, the ladder will reach a height of approximately 10.4 ft.
To solve this problem using the Pythagorean Theorem, we know that the ladder, the base of the ladder, and the height it reaches form a right triangle.
Let's denote the height of the ladder as 'h' (which is the unknown), the distance of the ladder's bottom from the base of the house as 'b' (which is given as 6 ft), and the length of the ladder as 'c' (which is given as 12 ft).
According to the Pythagorean Theorem, in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Therefore, we can write the equation as:
h^2 = c^2 - b^2
Substituting the given values into the equation:
h^2 = 12^2 - 6^2
h^2 = 144 - 36
h^2 = 108
To solve for 'h', take the square root of both sides:
h = √108
Rounding to the nearest tenth, we find that the ladder will reach approximately 10.4 ft.
So, the correct answer is 10.4 ft.