A ladder is leaning against a house. The distance between the base of the ladder to the house is 3 feet. The length of the ladder is 10 feet. In feet, how far above the ground does the ladder touch the house?
4.2
9.5
10.4
14.1
a^2 + b^2 = c^2
2^2 + b^2 = 10^2
4 + b^2 = 100
b^2 = 96
b = 9.8 feet
To find out how far above the ground the ladder touches the house, we need to use the Pythagorean theorem. The Pythagorean theorem 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, the ladder represents the hypotenuse, and the distance between the base of the ladder and the house represents one of the other sides.
Using the Pythagorean theorem, we can calculate the length of the third side (the height of the ladder above the ground) as follows:
Length of the third side^2 = Length of the ladder^2 - Distance between the base and the house^2
Length of the third side^2 = 10^2 - 3^2 = 100 - 9 = 91
Taking the square root of both sides, we find:
Length of the third side = √91 ≈ 9.54.
Therefore, the ladder touches the house at a height of approximately 9.54 feet above the ground.
None of the provided options exactly match the calculated value, but the option closest to 9.54 feet is 9.5.