Advances in International Applied Mathematics

This paper focuses on triangle‐solving problems in the mathematics section of the National College Entrance Examination, aiming to systematically analyze their problem‐type characteristics and solution strategies. By reviewing Gaokao mathematics papers from the past five years, five representative problem types are identified: side‐angle interchange, area computation, extremum analysis, determination of value ranges, and integrated applications. For each category, a case‐analysis approach is employed, examining authentic exam questions step by step and summarizing the corresponding strategies, with particular emphasis on the flexible application of the law of sines, the law of cosines, trigonometric identity transformations, and algebraic methods. The findings of this study not only assist students in constructing a systematic problem‐solving framework and enhancing their ability to recognize problem types and transfer strategies, but also provide targeted guidance for high school mathematics instruction and Gaokao preparation.

Solving triangles; College entrance examination; Solution strategy; Law of sines; Law of cosines