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Question Number 187808 by LowLevelLump last updated on 22/Feb/23
Answered by a.lgnaoui last updated on 22/Feb/23
△ABC′{AB=AC=BC=aS1=a232△ACB′{AC=AB′=CB′=bS2=b232△BCC′{BC=BC′=CC′=cS3=c232sinB=AHAB=13⇒AH=asinBS1−S2+S3=(a2−b2+c2)32=32(1)S(△ABC)=c×AHAB2=ac6=(2){a2−b2+c2=1c=acosB+b2−a2sin2Bc=2a23+139b2−a2{c2=b2−a2+1(3)c=2a2+9b2−a23(4)b2=(9−16a2)2288a2+a29(3)⇒c2=1+(9−16a2)2288a2−8a29c2=81288a2⇒c=9224a(5)a)AreaABC=ac6=3248Area(ABC)=216b)IfsinAsinC=23sinAc=sinBb=sinCa⇒asinA=csinCa23sinC=csinC⇒3csin2C=a2sin2c=a23c;sinc=AHb=asinBb=a3b(sinB=13)=a29b2=a23cb2=ac26=(5)⇒b2=9224×26⇒b=24
Commented by a.lgnaoui last updated on 22/Feb/23
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