三角形ABC中，abc分别是内角ABC的对边 在三角形abc中,内角abc所对的边分别为abc,已知aco...
\u5df2\u77e5abc\u5206\u522b\u4e3a\u4e09\u89d2\u5f62ABC\u5185\u89d2ABC\u7684\u5bf9\u8fb9\uff0csin\u5e73\u65b9B=2sinAsinC1.\u2235A\u3001B\u3001C\u662f\u4e09\u89d2\u5f62\u7684\u4e09\u4e2a\u5185\u89d2
\u2234sinB\u22600\uff0cA+B+C=180\u00b0
\u2235a=b\uff0c\u5219A=B
\u2234C=\u03c0-2B ==>sinC=sin(2B)=2sinBcosB
\u2235(sinB)^2=2sinAsinC
==>(sinB)^2=2sinBsinC=4cosB(sinB)^2
==>(4cosB-1)(sinB)^2=0
==>4cosB-1=0
\u2234cosB=1/4\u3002
2.\u2235B=90\u00b0\uff0c(sinB)^2=2sinAsinC
==>2sinAsinC=1
==>2sinAsin(90\u00b0-A)=1
==>2sinAcosA=1
==>sin(2A)=1
==>2A=90\u00b0
==>A=45\u00b0
\u2234\u25b3ABC\u662f\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62\uff0ca=c
\u2235a=\u221a2
\u2234\u25b3ABC\u7684\u9762\u79ef=ab/2=a^2/2=1\u3002
\u6269\u5c55\u8d44\u6599\u4e09\u89d2\u5f62\u662f\u7531\u540c\u4e00\u5e73\u9762\u5185\u4e0d\u5728\u540c\u4e00\u76f4\u7ebf\u4e0a\u7684\u4e09\u6761\u7ebf\u6bb5\u2018\u9996\u5c3e\u2019\u987a\u6b21\u8fde\u63a5\u6240\u7ec4\u6210\u7684\u5c01\u95ed\u56fe\u5f62\uff0c\u5728\u6570\u5b66\u3001\u5efa\u7b51\u5b66\u6709\u5e94\u7528\u3002
\u5e38\u89c1\u7684\u4e09\u89d2\u5f62\u6309\u8fb9\u5206\u6709\u666e\u901a\u4e09\u89d2\u5f62\uff08\u4e09\u6761\u8fb9\u90fd\u4e0d\u76f8\u7b49\uff09\uff0c\u7b49\u8170\u4e09\u89d2\uff08\u8170\u4e0e\u5e95\u4e0d\u7b49\u7684\u7b49\u8170\u4e09\u89d2\u5f62\u3001\u8170\u4e0e\u5e95\u76f8\u7b49\u7684\u7b49\u8170\u4e09\u89d2\u5f62\u5373\u7b49\u8fb9\u4e09\u89d2\u5f62\uff09\uff1b\u6309\u89d2\u5206\u6709\u76f4\u89d2\u4e09\u89d2\u5f62\u3001\u9510\u89d2\u4e09\u89d2\u5f62\u3001\u949d\u89d2\u4e09\u89d2\u5f62\u7b49\uff0c\u5176\u4e2d\u9510\u89d2\u4e09\u89d2\u5f62\u548c\u949d\u89d2\u4e09\u89d2\u5f62\u7edf\u79f0\u659c\u4e09\u89d2\u5f62\u3002
(2016\u79cb•\u83cf\u6cfd\u671f\u672b)\u25b3ABC\u7684\u5185\u89d2A,B,C\u6240\u5bf9\u7684\u8fb9\u5206\u522b\u4e3aa,b,c,
acosC+ccosA=2bcosA.
(1)\u6c42A; (2)\u82e5a=\u221a7,b=2,\u6c42\u25b3ABC\u7684\u9762\u79ef.
\uff081\uff09acosC+ccosA=2bcosA.
\u5219 bc=2bccosA
cosA=1/2, A=60\u00b0
\uff082\uff09b^2+c^2-a^2=(2bc)cosA
4+c^2-7=2c
c^2-2c-3=0
c=3
S=bcsinA/2=6*\u221a3/4=3\u221a3/2
如上图所示。
绛旓細浣犲弬鑰冨弬鑰冨弬鑰冿紒
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