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ç®åºå¨é¿çä¸ås=1/2(a+b+c)
å该ä¸è§å½¢é¢ç§¯S=æ ¹å·[s(s-a)(s-b)(s-c)]
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设ä¸è§å½¢çä¸è¾¹aãbãcç对è§åå«ä¸ºAãBãCï¼
åæ ¹æ®ä½å¼¦å®çc²=a²+b²-2ab·cosC,å¾
cosC = (a²+b²-c²)/2ab
S=1/2*ab*sinC
=1/2*ab*â(1-cos²C)
=1/2*ab*â[1-(a²+b²-c²)²/4a²b²]
=1/4*â[4a²b²-(a²+b²-c²)²]
=1/4*â[(2ab+a²+b²-c²)(2ab-a²-b²+c²)]
=1/4*â{[(a+b)²-c²][c²-(a-b)²]}
=1/4*â[(a+b+c)(a+b-c)(a-b+c)(-a+b+c)]
设s=(a+b+c)/2
ås=(a+b+c), s-a=(-a+b+c)/2, s-b=(a-b+c)/2, s-c=(a+b-c)/2,
ä¸å¼=â[(a+b+c)(a+b-c)(a-b+c)(-a+b+c)/16]
=â[s(s-a)(s-b)(s-c)]
æ以ï¼ä¸è§å½¢ABCé¢ç§¯S=â[s(s-a)(s-b)(s-c)]
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