一类解三角形问题的又一解法

• 作 者: 雷风 彭玲
• 机 构: 萧县中学数学组,萧县中学数学组 安徽 235200,安徽 235200
• 出 处: 数学通讯
• 发表日期: 2005年01期
• 关键词: 判断准则 万晋 减函数 八门 三边

已知三角形的两边和其中一边的对角,判断三角形解的个数问题是学生学习的一个难点.对此问题,课本高一(下)P129给出了一个较难掌握的图解法,尽管文[1]也给予了详尽的归纳、指导,但依条件的不同,分类较多,判断准则各异,不太具有可操作性.于是,文[2]作者覃埋基老师独辟蹊径,借助余弦定理及二次方程知识给出了另一解法.笔者本着“三角问题三角解决”的想法,给出该类问题的再一种解法,仅供参考.

Knowing the two sides of the triangle and the diagonal of one side, judging the number of triangle solutions is a difficult problem for students to learn. To solve this problem, the textbook (a lower) P129 gives a graphic method that is difficult to grasp, although [1] also gave detailed induction and guidance, but according to the different conditions, there are more categories, different judgment criteria, and not very operability. And the knowledge of quadratic equations gives another solution. The author takes the idea of ​​“triangular triangulation” and gives a solution to this problem for reference only.