a/sinA=b/sinB=c/sinC=2R
sinB+sinC=(b+c)/2R
所以 b+c=2R*(sinB+sinC)=2R*4/3=2*6*4/3=16
S=a^2-(b-c)^2
=a^2-b^2-c^2+2bc
=2bc-2bccosA
=2bc(1-cosA)
S=1/滑世2*bc*sinA
所以桐野
1/2*bc*sinA=2bc(1-cosA)
sinA=4(1-cosA) .....(1)
sinA(1+cosA)=4*sinA*sinA
即 4sinA=1+cosA ......(2)
(1)+(2)*4,得
sinA+16sinA=8
sinA=8/17
S=1/2*bc*sinA
=4/17*bc<=4/17*((a+b)/2)=4/17*(16/2)^2=256/17
即 S的最大局让喊值是 256/17
S=a^2-(b-c)^2=-(b^2+c^2-a^2)+2bc=1/2bcsinA
联立迹缺悉4(1-cosA)=sinA,sin^2A+cos^2A=1,A≠0
解得cosA=15/17,sinA=8/17
b=2R*sinB,c=2R*sinC
b+c=12(sinB+sinC)=16
bc=b(16-b)=-(b-8)^2+64
s=1/扮帆2bcsinA=4/17[-(b-8)^2+64]
当b=8,sinB=2/3时
Smax=256/姿乎17