The results of this book's research provide compelling evidence of ChatGPT's adept use of the Peter Chew Rule, enabling give correct answer for Pool Game Obtuse problems and directly finding non included angle when furnished with two side lengths and an included angle. In contrast, when Chat GPT using the conventional approach, Chat GPT can not give correct answer solve the mention Pool Game Obtuse problems . This performance disparity underscores the vital role of the Peter Chew Ruled in enhancing AI systems' mathematical abilities, highlighting the trans formative potential of diverse methodologies in advancing AI's mathematical prowess. Pioneering Novel Maths Rule (Peter Chew Rule For Solution Of Triangle) for Overcoming Error in AI System . This study underscores the importance of pioneering innovative Rule to overcome existing Pool Game Obtuse Errors in AI systems like ChatGPT, particularly in solving problems involving determination the non included angle when furnished with two side lengths and an included angle. The groundbreaking Peter Chew Rule for Triangle Solution showcased here holds the promise of unleashing untapped potential, elevating AI systems to new levels of proficiency. Essentially, the Peter Chew Rule offers a strategic avenue for enhancing AI capabilities and pushing the boundaries of achievable accomplishments.