To solve for the height, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the ladder, one side is the distance from the base of the ladder to the house (6 ft), and the other side is the height we're trying to find (let's call it h).
So the equation will be:
(6 ft)^2 + h^2 = (12 ft)^2
36 ft^2 + h^2 = 144 ft^2
h^2 = 144 ft^2 - 36 ft^2
h^2 = 108 ft^2
To find h, we take the square root of both sides:
h = √108 ft^2
h ≈ 10.4 ft.
Therefore, the ladder will reach a height of approximately 10.4 ft.
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
180 ft.
180 ft.
10.4 ft.
10.4 ft.
108 ft.
108 ft.
13.4 ft.
1 answer