A 14-foot ladder is set up 4 feet from the base of the building. How far up the building does the ladder reach?

This problem creates a right Triangle the building is one side and the 4ft is the other side the ladder is the hypotenuse apply the Pythagorean Theorem'a^2 + b^2 = c^2 4^2 + b^2 = 14^2 16 + b^2 = 195 b^2 = 180 b = square root of 180 b = 6 square root of 5 or 13.42

Assuming it forms a right triangle with the side of the building, you could just use the Pythagorean Theorem to find the height. The ladder would be the hypotenuse, so you would substitute that as c into the equation. The 4 feet could be either a or b; it doesn't really matter. Plug it into (a^2) + (b^2) = (c^2), and you would get. (4^2) + (b^2) = (14^2); simplified, it is (16) + (b^2) = (196). Subtract 16 from 196 to get 180, and you see that (b^2) is equal to 180. Just take the square root of that to get your answer, which would be 6 sqrt5.