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 is equal to the sum of the squares of the lengths of the other two sides.
In this case, the ladder is the hypotenuse and the distance from the base of the house to the ladder is one of the other two sides. Let's call this distance x. The height that the ladder reaches will be the other side.
We can set up the equation as follows:
x^2 + 6^2 = 12^2
x^2 + 36 = 144
x^2 = 144 - 36
x^2 = 108
To find x, we can take the square root of both sides:
√x^2 = √108
x = √108
x ≈ 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.
108 ft.
108 ft.
10.4 ft.
10.4 ft.
13.4 ft.
1 answer