Question

(1/2)在△ABC中，角ABC的对边分别对应abc，若SinA SinB SinC成等比数列，且a2－c2＝ac－bc，求角A的...

(1/2)在△ABC中，角ABC的对边分别对应abc，若SinA SinB SinC成等比数列，且a2－c2＝ac－bc，求角A的大小及bS

Answer 1

sinA/sinB=sinB/sinC
a/b=b/c
b^2=ac
a^2-c^2=ac-bc=b^2-bc
b^2+c^2-a^2=bc
cosA=(b^2+c^2-a^2)/(2bc)
=bc/(2bc)
=1/2
∵A∈(0,π)
∴A=π/3