If the ladder makes a 45 degree angle with the building, then it also makes a 45 degree angle with the ground (45-45-90). The rule for the 45-45-90 is (x, x, xsqrt2). The sqrt2 is the hypotenuse measure, which is always the longest of the sides in a right triangle. If the hypotenuse is 12, set up your equation like this: [tex]12=x \sqrt2[/tex] In order to undo that square root, square both sides, getting [tex]144=2 x^{2} [/tex] Now divide both sides by 2 to get [tex]72= x^{2} [/tex] and take the square root of both sides and simplify. The square root of 72 simplified is [tex] 6 \sqrt2[/tex]
