Solve the following problem. (See Examples 8 and 9).A 13-foot-long ladder leans on a wall,...

Solve the following problem. (See Examples 8 and 9).

A 13-foot-long ladder leans on a wall, as shown in the accompanying figure. The bottom of the ladder is 5 feet from the wall. If the bottom is pulled out 2 feet farther from the wall, how far does the lop of the ladder move down the wall? [Hint: Draw pictures of the right triangle formed by the ladder, the ground, and the wall before and after the ladder is moved. In each case, use the Pythagorean theorem to find the distance from the top of the ladder to the ground.]