在三角形abc中,内角A,B,C的对边分别是a,b,c,若a눀-b눀=√3bc,sinC=2√3sinB,则A=

2024-12-04 21:14:26
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回答1:

c=2RsinC, sinC=c/2R
b=2RsinB, sinB=b/2R
sinC=2√3sinB, c/2R=2√3*b/2R
c=2√3b
a^2=b^2+c^2-2bc*cosA
a^2-b^2=c^2-2bc*cosA
√3bc=c^2-2bc*cosA
√3b*2√3b=12b^2-2b*2√3b*cosA
6b^2=12b^2-4√3b^2cosA
cosA=√3/2
A=30