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?
We have the bottom of the ladder, the top of the ladder, and the distance from the base of the house forming a right triangle. The height above the ground is the height of this triangle. This can be found using the Pythagorean Theorem. The length of the hypotenuse, the ladder, is 30 feet, and the base is 7 feet. The height is the unknown we're trying to find, so we'll call it $h$. Putting this into the Pythagorean theorem, we get $h^2 + 7^2 = 30^2$. Simplifying the equation gives $h^2 = 30^2 - 7^2 = 900 - 49 = 851$. Since we want the height to the nearest tenth of a foot, we take the square root of 851 and round to the nearest tenth to find that $h\approx \boxed{29.1}$ feet.
