(1⼀2)已知三角形ABC的周长为根号2+1,且sinA+sinB=根号2sinC,1.求边c的长.2.三角形ABC的面积为1⼀6sinC...

2025-05-13 12:40:39
推荐回答(1个)
回答1:

a/sinA=b/sinB=c/sinC=k
sinA+sinB=√2sinC
a+b=√2c
a+b+c=√2+1
c=1
a+b=√2
S=(1/2)absinC=(1/6)sinC
ab=1/3
cosC=(a^2+b^2-c^2)/2ab=[(a+b)^2-2ab-c^2]/2ab=(2-1-2/3)/2*(1/3)=1/2
C=60