在△ABC中,角A,B,C的对边分别为a,b,c,且满足根号3sinA-cosA=0,cosB=4/5,b=2根号3

答
√3sinA-cosA=0
√3sinA=cosA
sinA/cosA=1/√3
∴tanA=√3/3
∵A是内角
∴A∈(0,π)
∴A=π/6
(2)
cosB=4/5
∴sinB=3/5
正弦定理
b/sinB=a/sinA
2√3/(3/5)=a/(1/2)
a=5√3/3
sinC
=sin(A+B)
=sinAcosB+cosAsinB
=1/2*4/5+√3/2*3/5
=(4+3√3)/10
△ABC的面积
=1/2*ab*sinC
=(4+3√3)/2