这道题好怪,应该是等差数列吧,三角形内角成等比数列在百度知道类似的题目中第一次见.
(1)
A、B、C成等差数列,则
2B=A+C
又A+B+C=180°
3B=180°
B=60°
SΔABC=(1/2)acsinB=(1/2)acsin60°=(1/2)ac(√3/2)= √ 3/2
ac=2
(2)
由正弦定理b/sinB=a/sinA=c/sinC
a/sinA=c/sinC=√3/(√3/2)=2
a=2sinA c=2sinC
ac=4sinAsinC=2
sinAsinC=1/2
[cos(A-C)-cos(A+C)]/2=1/2
cos(A-C)-cos(A+c)=1
cos(A-C)+cos(180°-B)=1
cos(A-C)=1-cos(180°-B)=1-1/2=1/2
A-C=60°
A=C+60°
A+B+C=2C+60°+60°=180°
C=30°
A=30°+60°=90°
a=2sinA=2 c=2sinC=1