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)
Responses
28.9 ft.
28.9 ft.
22.0 ft.
22.0 ft.
31.0 ft.
31.0 ft.
27.8 ft.
27.8 ft.
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To solve this problem, we can use the Pythagorean theorem.
The ladder, the distance from the foot of the ladder to the base of the house, and the distance from the top of the ladder to the top of the house form a right triangle.
Let x be the height above the ground that the top of the ladder touches the house.
Using the Pythagorean theorem, we have:
x^2 + 8^2 = 30^2
x^2 + 64 = 900
x^2 = 836
x ≈ 28.9
Therefore, the top of the ladder is approximately 28.9 feet above the ground.
The correct answer is 28.9 ft.