在△ABC中,角A,B,C所对边分别为a,b,c,且向量
=(sinA,sinB),
=(cosB,cosA),满足
•
=sin2C.
(1)求角C的大小;
(2)若sinA,sinC,sinB成等差数列,且
•(−)=18,求边c的长.
(1)m•n=sinAcosB+sinBcosA=sin(A+B)对于△ABC,A+B=π-C,0<C<π,∴sin(A+B)=sinC∴m•n=sinC又∵m•n=sin2C,∴sin2C=2sinCcosC=sinC,即cosC=12,又C∈(0,π)∴C=π3;(2)由sinA,sinC,sinB成...