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.