Question

在△ABC中内角A,B,C的对边分别为a，b，c,sinC/sinA=2 cosB=1/4且△ABC的周长为5。求边b的长

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Answer 1

cosB=1/4 =>sinB=根号15/4
sinC=sin(B+A)=sinBcosA+cosBsinA=根号15/4cosA+1/4sinA=2sinA (利用前面的结果)
=>根号15/4*cosA=7/4*sinA
=>tanA=根号15/7
=>sinA=根号15/8
=>sinC=根号15/4
=>a:b:c=sinA:sinB:sinC=根号15/8:根号15/4:根号15/4
=1:2:2
a+b+c=5
=>a=1 b=2 c=2