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向量=1+√3,求a,b,c

问题描述:

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向量=1+√3,求a,b,c

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/42.∵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...