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.
To find the height that the ladder will reach, we can use the Pythagorean Theorem:
a^2 + b^2 = c^2
where a is the distance from the base of the ladder to the house (6 ft), b is the height the ladder reaches, and c is the length of the ladder (12 ft).
So, plugging in the given values:
6^2 + b^2 = 12^2
36 + b^2 = 144
b^2 = 144 - 36
b^2 = 108
Taking the square root of both sides to solve for b:
b = √108 ≈ 10.4 ft.
Therefore, the ladder will reach a height of approximately 10.4 ft.