Question

一道解三角形（纯计算那种，图片）的题目

Answer 1

1.
根据正弦定理，a/sinA=b/sinB=c/sinC=2R
将已知条件两边除以2R（外接圆半径）
=》3sinAcosA=sinCcosB+cosCsinB=sin(B+C)=sin(180-A)=sinA
=》cosA=1/3
2.
cosA=1/3
=》sinA=2√2/3
cosB=cos(180-A-C)=-cosAcosC+sinAsinC=-cosC/3+2√2/3sinC
cosB+cosC=2cosC/3+2√2/3sinC=2√3/3(1/√3cosC+√2/√3sinC)=2√3/3
=》
=》1/√3cosC+√2/√3sinC=1
=》sin(θ+C)=1
其中cos(θ)=√2/√3
=》θ+C=PI/2
=》sinC=cos(θ)=√2/√3
根据正弦定理，c/sinC=a/sinA=>c=a/sinA*sinC=1/[2√2/3]*[√2/√3]
=√3/2