(1)由cosA=3/4,得sinA=√7/4;
cosC=cos(2A)=2cos²A-1=2*(3/4)²-1=1/8;sinC=3√7/8;
cosB=-cos(A+C)=sinAsinC-cosAcosC=(√7/4)*(3√7/8)-(3/4)*(1/8)=9/16;
(2)由题意,向量BA*向量BC=27/2=2ac*cosB;
ac=27/(4cosB)=27/(4*9/16)=12,
根据正弦定理,a/sinA=c/sinC,a=c*sinA/sinC=2c/3;
以上两式联解得:a=2√2,c=3√2;
由余弦定理:b²=a²+c²-2ac*cosB=(2√2)²+(3√2)²-27/2=21/2,b=√42/2;
追问第二问你算错了,b=5
追答向量乘积代错了,后面没有两倍:向量BA*向量BC=27/2=ac*cosB;抱歉!