三线段能构成锐(钝)角三角形的条件

• 作 者: 王曦
• 机 构: 江西省永丰中学高三(8)班,
• 出 处: 中学数学研究
• 发表日期: 2016年01期
• 关键词: 取值范围 锐角三角形

1、问题的提出先来看以下例题及其解法.例1(1)已知锐角三角形的三边长分别为2,3,x,求x的取值范围;(2)已知钝角三角形的三边长分别为2,3,x,求x的取值范围.解:(1)(法一)因为三角形是锐角三角形,所以三个角均为锐角,由余弦定理知2~2+3~2-x~2>0,2~2

1, the problem is raised first look at the following example and its solution.Example 1 (1) known triangle triangle length were 2,3, x, x value range; (2) known obtuse triangle Solution: (1) (Method 1) Because the triangle is an acute triangle, the three corners are all acute angles, and the cosine theorem knows 2 ~ 2 + 3 ~ 2-x ~ 2> 0,2 ~ 2