1.(1)由正弦定理,得cosB/cosC=-sinB/(2sinA+sinC),可得

sinA(2cosB+1)=0,∵A≠0,∴cosB=-1/2,B=2π/3.

(2)cosB=(a²+c²-b²)/(2ac)=-1/2,∴ac=3,a+c=4,解得

a=1或a3.

2.sinβ=(2/3)sinα=√2/3,cosβ=√7/3,行程=1/d=3/√7=1.134厘米.

3.详细解答过程如下图所示