来自陈在礼的问题
已知三角形ABC的周长为根号2+1且sinA+sinB=根号2sinC.求:1求边AB的长.2若sinAsinB=1/3sin^2C求角C的大小
已知三角形ABC的周长为根号2+1且sinA+sinB=根号2sinC.求:1求边AB的长.2若sinAsinB=1/3sin^2C求角C的大小
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2020-04-16 22:20
已知三角形ABC的周长为根号2+1且sinA+sinB=根号2sinC.求:1求边AB的长.2若sinAsinB=1/3sin^2C求角C的大小
已知三角形ABC的周长为根号2+1且sinA+sinB=根号2sinC.求:1求边AB的长.2若sinAsinB=1/3sin^2C求角C的大小
1、R(sinA+sinB+sinC)=2^0.5+1
因为sinA+sinB=2^0.5sinC
故R[2^0.5+1]sinC=2^0.5+1
则RsinC=1,即AB=1
2cosC=(a*a+b*b-c*c)/2a*b=(sinA*sinA+sinB*sinB-sinC*sinC)/2sinA*sinB
=[(sinA+sinB)^2-2sinA*sinB-sinC*sinC]/2*sinA*sinB
=[2sinC^2-2/3sinC^2-sinC^2]/2/3sinC^2
=1/3/(2/3)
=1/2
因为0