Five typical question types of triangle solving problems in the college entrance examination and their solution strategies
高考中解三角形问题的五种典型题型及求解策略

摘要

本文以高考数学中解三角形问题为研究对象，旨在系统分析其题型特征与解题策略。通过梳理近五年全国高考试卷，归纳出五类典型题型：边角互换、面积计算、最值分析、取值范围和综合应用。针对每一类别，本文采用案例分析法，结合真题逐题剖析解题思路，并总结出相应策略，重点强调正弦定理、余弦定理、三角恒等变换及代数方法的灵活应用。该研究既有助于学生构建系统化的解题路径，提升题型识别与策略迁移能力，也可为高中数学教学与高考备考提供针对性参考。

Abstract

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.