Nicholas places his 30-foot ladder against a house he is painting. If the foot of the ladder is 8 feet from the base of the house, how high above the ground is the top of the ladder touching the house, to the nearest tenth of a foot?(1 point)%0D%0AResponses%0D%0A%0D%0A28.9 ft.%0D%0A28.9 ft.%0D%0A%0D%0A27.8 ft.%0D%0A27.8 ft.%0D%0A%0D%0A31.0 ft.%0D%0A31.0 ft.%0D%0A%0D%0A22.0 ft.
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 (in this case, the ladder) is equal to the sum of the squares of the other two sides.
In this case, one side of the right triangle is the 8-foot distance from the base of the ladder to the house. The other side is the height of the ladder touching the house, which we need to find. The ladder itself is the hypotenuse.
Using the Pythagorean theorem, we have:
(8)^2 + (height)^2 = (30)^2
Simplifying this equation, we get:
64 + (height)^2 = 900
Subtracting 64 from both sides, we have:
(height)^2 = 836
Taking the square root of both sides, we get:
height = sqrt(836) ≈ 28.9 ft.
Therefore, the top of the ladder is touching the house at a height of approximately 28.9 feet.
So, the answer is 28.9 ft.