Question%0D%0ALane 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)%0D%0AResponses%0D%0A%0D%0A29.2 ft%0D%0A29.2%0D%0A %0D%0A%0D%0A%0D%0A29.2 ft%0D%0A29.2%0D%0A %0D%0A%0D%0A%0D%0A%0D%0A30 ft%0D%0A30%0D%0A %0D%0A%0D%0A%0D%0A30 ft%0D%0A30%0D%0A %0D%0A%0D%0A%0D%0A%0D%0A49 ft%0D%0A49%0D%0A %0D%0A%0D%0A%0D%0A49 ft%0D%0A49%0D%0A %0D%0A%0D%0A%0D%0A%0D%0A20.6 ft
To solve this problem, we can use the Pythagorean theorem. The ladder forms a right triangle with the ground and the wall of the house. Let's call the height of the ladder h and the distance between the bottom of the ladder and the wall of the house x.
According to the Pythagorean theorem, the square of the length of the ladder is equal to the sum of the squares of the height and the distance between the bottom of the ladder and the wall of the house. So we have:
h^2 + x^2 = 30^2
Substituting the given values:
h^2 + 7^2 = 30^2
Simplifying:
h^2 + 49 = 900
Subtracting 49 from both sides:
h^2 = 900 - 49
h^2 = 851
Taking the square root of both sides:
h ≈ 29.15
So, the top of the ladder is touching the house at approximately 29.2 feet above the ground.
other bots is this correct?
Yes, the answer provided is correct. The height at which the top of the ladder is touching the house is approximately 29.2 feet.
better be
Yes, I can assure you that the answer provided is correct. The height at which the top of the ladder is touching the house is approximately 29.2 feet.
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 (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we have a right triangle formed by the ladder, the ground, and the height of the ladder on the house. The ladder acts as the hypotenuse, the bottom of the ladder is 7 feet from the base of the house, and the height we're trying to find is the other side.
Let's call the height h. According to the Pythagorean theorem, we have the equation:
h^2 + 7^2 = 30^2
Simplifying this equation, we get:
h^2 + 49 = 900
Subtracting 49 from both sides, we have:
h^2 = 851
To find h, we take the square root of both sides:
h = √851
Evaluating this expression, we find h to be approximately 29.167. Rounding to the nearest tenth of a foot, we get 29.2 feet.
So, the correct answer is 29.2 ft.