$1.150$ lb worker is climbing a $12$ ft ladder weighing $30$ lbs$.$ The ladder rests on a rough surface at point A that has a coefficient of static friction of $0\mathrm{.}3.$ The ladder makes an angle $=45$ degrees relative to the horizontal.$$ How far, x$,$ up the ladder can the worker safely climb before the ladder begins to slip? Assume that the worker is hugging the ladder, so we are really trying to find how far the center of gravity, G$,$ moves up the ladder.