在△ABC中,角A,B,C的对边分别是a,b,c,且acosB=(3c-bcosA)

2025-01-21 02:50:40
推荐回答(1个)
回答1:

acosB=(3c-b)cosA

sinAcosB=3sinCcosA-sinBcosA
sinAcosB+sinBcosA=3sinC
sin(A+B)=3sinCcosA
sinC=3sinCcosA
cosA=1/3
sinA=√[1-(cosA)^2]=2√2/3
a/sinA=b/sinB
bsinA=asinB

b=asinB/sinA==2√2/(2√2/3)=3
b=3
2)S=1/2bcsinA=√2

1/2bc*2√2/3=√2
bc=3
b^2+c^2-2bc*(1/3)=(2√2)^2

(b+c)^2-(8/3)bc=8
(b+c)^2=8+(8/3)bc
(b+c)^2=8+(8/3)*3
(b+c)^2=16
b+c=4
a+b+c=4+2√2