Saturday 5 April, 2008

Equilateral Triangle

How can you prove that a triangle is equilateral if and only if
tan A + tan B + tan C = 3√3 ?
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2 comments:

Ananth said...

Hint: Related to a chapter in Module - 3 (Mathematics).

7 April 2008 at 2:35 pm
Ananth said...

If the given triangle is equilateral
A=B=C=60, or tan A + tan B + tan C = 3 root 3.

On the other hand, if
tan A + tan B + tan C = 3 root 3.
As A+B+C=180,
tan A . tan B . tan C = 3 root 3.

A.M. = G.M. = root 3.
Thus, tan A = tan B = tan C or A=B=C=60

Hence proved both ways, or proved that a triangle is equilateral iff (if and only if) tan A + tan B + tan C = 3 root 3.

10 April 2008 at 9:09 pm

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