20 12 dongyang middle school simulation test math (science) question 18 detailed answer ……………………………………………………………………………………………………………………………………….

Solution: (1) ∵ in Δ Δ ABC, ∠ a.

∴2B=A+C,A+B+C= 180，

∴B=60，A=60 -θ，C=60 +θ

And ∵ 1/SINA, 3 √ 2/2 SINB, 1/SINC became arithmetic progression.

∴3√2/sinb= 1/sina+ 1/sinc

2√6 = 1/sin(60-θ)+ 1/sin(60+θ)

cosθ/[(cosθ)^2- 1/4]=√2

The solution is cosθ=√2/2 or -√2/4 (abbreviated).

∴θ=45

(2) sinA/a=sinB/b=sinC/c can be obtained by sine theorem,

A=(√6-√2)

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