Here is another way to find the direction of the cue ball off the object ball for a rolling cue ball. That's the sort of shot that you use the peace sign or the 3x angle ideas for. Those methods are restricted to ranges of angles. The following method works for all angles.
In the diagram the 1 ball into the side is set up for about a half-ball example shot. Position 1 of the cue stick is with the stick parallel to the path of the object ball and the tip even with the ghost ball. The rectangle shows those relationships. (Of course if the 1 ball were not going straight across the table, putting the cue stick correctly is much harder.)
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The easy way to get there is to put the cue stick with the tip at the ghost ball along the line of the shot and move it up in parallel. Move it until the bumper, the cue ball and the ghost ball are in a straight line. It is always possible to do this.
If a point on the cue stick 1/4th of the way from the tip is marked (or estimated by halving twice), the line from that point through the ghost ball will give the line of the cue ball off the object ball.
For some shots it easier to use the cue stick in Position 2. In that case it is the 1/4th mark that is lined up with the cue ball and the ghost ball as shown. Now it is the bumper that gives the direction of the cue ball.
This method takes a while to learn. It is always possible to place the cue stick in each of the positions. Note that for each position the tip and butt can only be in one place. The cue stick must be either perpendicular or parallel to the path of the object ball and the tip (or bumper if you turn the cue around) must be even with the ghost ball. The cue stick will rarely be parallel to a cushion -- that's just true in the example shot to make the geometry clearer.
Note that for the Position 2 example, you can use the diamonds because the diamonds run perpendicular to the path of the object ball -- very convenient. Since the cue ball is starting out to 1 diamond from the side pocket, after the collision it is deflected three more diamonds down the table.
It might be easier to use a 1/4th spot on the butt rather than the shaft and a suitable mark may already be on your cue stick.
Also, there is nothing magic about the length of the cue stick for this geometry. You could do the same thing with just the length of the shaft. Or, you could use four hand spans.