在三角形ABC中,若b=2a,B=A+π/3,则角A=

问题描述:

在三角形ABC中,若b=2a,B=A+π/3,则角A=

b/a=sinB/sinA=2
sinB=2sinA
sinB=sin(A+π/3)
=sinAcosπ/3+cosAsinπ/3=2sinA
(3/2)sinA=√3/2cosA
tanA=sinA/cosA=√3/3
所以A=π/6