You are told that in a billiards shot, the cue ball was shot at the eight ball, which was 8 inches away. As a result, the eight ball rolled into a pocket, which was 6 inches away. Knowing that the angle made with the path of the cue ball and the resulting path of the eight ball is larger than \( 90^{\circ} \), it can be determined that the original distance from the cue ball to the pocket was greater than \( \square \)

Did you know that the game of billiards dates back to the 15th century? It was originally played outdoors on grass with wooden balls, and the aim was to knock balls into holes using a wooden stick. The indoor version we enjoy today evolved in France, leading to the creation of various types including pool and snooker. So next time you're playing, remember, you're part of a long and engaging history! When playing billiards, it's essential to calculate angles and distances accurately to improve your game. A common mistake many beginners make is underestimating the effect of angles on ball trajectories. To avoid this, always visualize the path of your shot while considering where you want the object ball (like the eight ball) to go. This spatial awareness can transform your gameplay and help you become a pro in no time!