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ï¼1ï¼ç±æ£å¼¦å®ça/sinA=b/sinB=c/sinCç¥ï¼è®¾æ¯ä¾ç³»æ°ä¸ºk,åa=KsinA,b=ksinB,c=ksinC
æ以ksinAcosC+â3ksinAsinC-ksinB-ksinC=0
å¾sinAcosC+â3sinAsinC-sinB-sinC=0
åBï¼Ï-(A+C),æ以sinB=sin[Ï-(A+C)]=sin(A+C)=sinAcosC+cosAsinC
æ以sinAcosC+â3sinAsinC-sinAcosC-cosAsinC-sinC=0
æ以sinC(â3sinA-cosA-1)=0
åsinCâ 0,
æ以â3sinA-cosA-1=0,å³â3sinA-cosA=1
å¾2sin(A-Ï/6)=1
æ以sin(A-Ï/6)=1/2,åA为ä¸è§å½¢å
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æ以Aï¼Ï/3
ï¼2ï¼å·²ç¥a=2ï¼Sï¼â3ï¼(1/2)absinC=(1/2)bcsinA=(1/2)acsinB
æ以(1/2)bcsin(Ï/3)=â3
æ以bc=4
ç±ä½å¼¦å®çï¼å¾a^2=b^2+c^2-2bccosA=b^2+c^2-2*4*(1/2)=b^2+c^2-4
åa=2ï¼æ以8=b^2+c^2
åbc=4, å¾c=4/b
æ以b^2+16/b^2=8
å³b^4-8b^2+16=0
(b^2-4)^2=0
æ以b^2=4ï¼å¾b=2ï¼æ以c=2
å³b=2, c=2
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