名校
1 . 秦九韶,字道古,鲁郡(今河南范县)人.中国古代数学家.他是一位非常聪明的人,处处留心,好学不倦.时人说他“性极机巧,星象、音律、算术,以至营造等事,无不精究”,秦九韶还创用了“三斜求积术”等,给出了已知三角形三边求三角形面积公式,与古希腊数学家海伦(Heron,公元50年前后)公式完全一致.学习数学,就要“知其然,知其所以然.”请你用所学的解三角形知识,推导证明海伦-秦九韶公式:
,其中
,
,
,
分别为
中角
,
,
所对的边.
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