Question

2012东阳中学模拟考试数学（理）的第18题求详细解答···在线等答案额················

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Answer 1

解：(1)∵在ΔABC中，∠A<∠B<∠C,且A,B,C成等差数列，公差为θ
∴2B=A+C,A+B+C=180°,
∴B=60°,A=60°-θ,C=60°+θ
又∵1/sinA,3√2/2sinB,1/sinC成等差数列
∴3√2/sinB=1/sinA+1/sinC
2√6=1/sin(60°-θ)+1/sin(60°+θ)
cosθ/[(cosθ)^2-1/4]=√2
解得cosθ=√2/2或-√2/4（舍去）
∴θ=45°
(2)由正弦定理可得sinA/a=sinB/b=sinC/c,
又a=(√6-√2)
则得sinA=sin(60°-45°)=(√6-√2)/4, sinB=sin60°=√3/2，sinC=sin(60°+θ)=(√6+√2)/4,b=2√3,
∴S=1/2absinC=1/2*(√6-√2)*2√3*(√6+√2)=√3