To solve this problem, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the ladder forms a right triangle with the ground and the wall of the house. The ladder is the hypotenuse, the distance from the base of the ladder to the wall is the height, and the distance from the base of the ladder to the ground is the base.
We are given that the base of the ladder is 5 feet and the ladder is 20 feet long.
Using the Pythagorean Theorem, we can solve for the height:
height^2 + 5^2 = 20^2
height^2 + 25 = 400
height^2 = 400 - 25
height^2 = 375
Taking the square root of both sides, we find:
height ≈ √375
height ≈ 19.4
Therefore, the top of the ladder is touching the house approximately 19.4 feet above the ground.
Scout places his 20-foot step ladder against a house he is painting. If the bottom of the ladder is 5 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)
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