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In triangle ABC, if tanA+tanB+tanC=6 and tanA.tanB=2 then trianlge is?
Answer is acute angled..Please explain how..
tanA and tanB is either both positive or both negetive from tanAxtanB=2
tanA+tanB+tanC=tanA x tanB x tanC=6
thus tanC is 4.thus c is acute.
since angle c is acute we can say that b and a will also be acute because both will be simultaneously positive and hence the triangle is acute.
A+B+C=180
A+B=180-C
Tan(A+B)=-TanC
(TanA+TanB)/(1-TanATanB)=-TanC
TanA+TanB+TanC=TanATanBTanC=6
TanC=3. so the angle C is acute.
TanA+TanB=3
TanA-TanB=1
therefore TanA=2 and TanB=1
A and B are also acute.
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