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.
10.4 ft.
10.4 ft.
180 ft.
180 ft.
To find the height that the ladder will reach, we can use the Pythagorean Theorem. According to the theorem, a^2 + b^2 = c^2, where a and b are the lengths of the sides of a right triangle, and c is the length of the hypotenuse (in this case, the ladder).
In this scenario, a = 6 ft. (the distance from the base of the house to the bottom of the ladder) and c = 12 ft. (the length of the ladder). We're trying to find b, which represents the height the ladder will reach.
Using the Pythagorean Theorem:
(6 ft.)^2 + b^2 = (12 ft.)^2
36 ft. + b^2 = 144 ft.
b^2 = 144 ft. - 36 ft.
b^2 = 108 ft.
b ≈ √(108 ft.)
b ≈ 10.4 ft.
Therefore, the ladder will reach a height of approximately 10.4 ft. So the correct response is:
10.4 ft.