三角形ABC中,A,B,C所对的边分别为a,b,c,A=∏/6,(1+√3)c=2b,(1)求C(2)若CB向量×CA向

1.∵A=π/6.∴B+C=5π/6.
(1+√3)c=2b → （1+√3）sinC=2sinB=2sin(150°-C)=cosC+√3sinC
→ sinC=cosC
→C=π/4
2.∵CB向量×CA向量=1+√3.
∴abcosC=1+√3=2b/c
∴ac=√2.①
∵a/sinA=b/sinB=c/sinC
∴a/(1/2)=b/sin105°=c/(√2/2) ②
→ a=1,c=√2,b=(√6+√2)/2.