7.已知三角形ABC的三边a>b>c且a+c=2b,A—C=90°,求a:b:c
问题描述：
7.已知三角形ABC的三边a>b>c且a+c=2b,A—C=90°,求a:b:c
8．在三角形ABC中,若(a+b+c)(a—b+c)=3ac,且tanA+tanC=3+根号3,AB边上的高为4根号3,求角A,B,C的大小与a,b,c的长
答
1.a+c=2b=>sinA+sinC=2sinB=>2sin(A+C)/2cos(A-C)/2=4sin(A+C)/2cos(A+C)/2又因0cos(π-B)/2=√2/4sinB/2=√2/4cosB/2=√[1-sin²(B/2)]=√14/4sinB=2(√2/4)(√14/4)=√7/4sinA*sinC=[cos(A-C)-cos(A+C)]/2=[2c...