三角形ABC中,已知a,b,c成等差数列,sinA,sinB,sinC成等比数列,试判断三角形ABC的形状

问题描述:

三角形ABC中,已知a,b,c成等差数列,sinA,sinB,sinC成等比数列,试判断三角形ABC的形状

a,b,c成等差数列:2b=a+cb/sinB=a/sinA=c/sinC=2R2sinB=sinA+sinCsinB=(sinA+sinC)/2sinA,sinB,sinC成等比数列:sin^2B=sinA*sinC[(sinA+sinC)/2]^2=sinA*sinC(sinA-sinC)^2=0sinA=sinCA=B=C=60°等边三角形...