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?
Using the Pythagorean theorem, we can solve for the height of the ladder touching the house.
Let the height of the ladder touching the house be 'h'. According to the problem, the base of the ladder is 7 feet away from the house.
Using the Pythagorean theorem, we have:
h^2 + 7^2 = 30^2
h^2 + 49 = 900
h^2 = 900 - 49
h^2 = 851
Taking the square root of both sides, we have:
h ≈ √851
h ≈ 29.1
Therefore, the height above the ground at which the top of the ladder is touching the house is approximately 29.1 feet.