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Heptagonal Triangle (Posted on 2019-12-27) Difficulty: 4 of 5
Let the vertices of △ABC be coinciding with the first, second and fourth vertices of a regular heptagon.

Find tan A + tan B + tan C.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution Comment 4 of 4 |
(In reply to Solution by Brian Smith)

To B. Smith

I sincerely hope you don't mind a bit of black humor. Your "elegant" solution brought to my mind a quote from the novel "The Heart of Darkness". The line is "The horror, the horror!"

In all fairness, I must admit that the answer -sqrt(7) has a poignant beauty with regard to a heptagon. (And is likely what DAK had in mind.)
But, I also think my tangents were OK and give the same result, but only just approximately.  - Cheers SL

  Posted by Steven Lord on 2019-12-28 16:19:38
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