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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..

In triangle ABC, if  tanA+tanB+tanC=6  and  tanA.tanB=2  then trianlge is?


Answer is acute angled..Please explain how..

Grade:12

2 Answers

Gaurav P
34 Points
9 years ago

 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.

G Narayana Raju
51 Points
9 years ago

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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