已知△ABC的三边为a,b,c,a+b=3,ab=2,且C=126°

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已知△ABC的三边为a,b,c,a+b=3,ab=2,且C=126°

已知△ABC的三边为a,b,c,a+b=3,ab=2,且C=126°
已知△ABC的三边为a,b,c,a+b=3,ab=2,且C=126°

已知△ABC的三边为a,b,c,a+b=3,ab=2,且C=126°
应该是C=120°
a=1,b=2或a=2,b=1
c^2=a^2+b^2-2ab(-1/2)=7
c=根号7

(1)用余弦定理:
c^2=a^2+b^2-2abcosC
=(a+b)^2-2ab-2abcosC
=9-4-4cos120°
=5+4*(1/2)
=7
c=√7
(2)S=(1/2)absinC
=(1/2)*2*(√3/2)
=√3/2