Lane places his 30-foot ladder against a house he is painting. If the bottom of the ladder is 7 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
29.2 ft
30 ft
49 ft
20.6 ft
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's call the height of the ladder x.
The bottom of the ladder forms the base of a right triangle, with the ladder itself as the hypotenuse, and the distance from the base of the house as one of the other sides.
Using the Pythagorean theorem, we can set up the equation:
x^2 = 30^2 - 7^2
x^2 = 900 - 49
x^2 = 851
x ≈ √851
x ≈ 29.2
Therefore, to the nearest tenth of a foot, the top of the ladder is approximately 29.2 feet above the ground.