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读本刊1992年第5期《中国的海伦公式》一文,颇受启发,由初中生熟知的三角形面积公式 S_△=1/2bcsinA=1/2acsinB=1/2absinC, 结合“中国的海伦公式”,即 S_△=(1/4[c~2a~2-((c~2+a~2-b~2)/2)~2])~(1/2), 不难得出如下一组公式: sinA=1/bc((c~2a~2-((c~2+a~2-b~2)/2)~2)~(1/2));① sinB=1/ac((c~2a~2-((c~2+a~2-b~2)/2)~2)~(1/2));② sinC=1/ab((c~2a~2-((c~2+a~2-b~2)/2)~2)~(1/2))。③应用这组公式,可以巧妙简捷地解决已知三角形三边长,求其内角一类题目,下面以一此典型题目为例,介绍这类题目的解法。例1 已知a=20,b=29,c=21,求角B。(初中《代数》第四册第144页第1题)
The article entitled “The Helen Formula of China” published in the 5th issue of 1992 is inspiring. The triangle area formula S_△=1/2bcsinA=1/2acsinB=1/2absinC, which is well known to junior high school students, is a combination of the “Chinese Helen formula”. , ie, S_Δ=(1/4[c~2a~2-((c~2+a~2-b~2)/2)~2])~(1/2), it is not difficult to Formula: sinA=1/bc((c~2a~2-((c~2+a~2-b~2)/2)~2)~(1/2)); 1 sinB=1/ac( (c~2a~2-((c~2+a~2-b~2)/2)~2)~(1/2)); 2 sinC=1/ab((c~2a~2-( (c~2+a~2-b~2)/2)~2)~(1/2)). 3 Applying this set of formulae can solve the problem of knowing the three sides of the known triangle and finding the internal angle. Example 1 is known to have a=20, b=29, c=21, and seek angle B. (The junior high school “Algebra” Volume 4 Issue 144, Problem 1)