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.
All numbers below are approximate.
The interior angles are (180 deg - 360 deg /7) = 128.57 deg
There are four chords extending from C to vertices. They evenly split the interior angle into five angles of 25.71 deg apiece. So C= 25.71 deg
Likewise angle B contains the sum of four such angles: So, B = 102.87 deg and A contains two: A= 51.42 deg
answer = tan(25.71) + tan(102.87) + tan(51.42)
I pause here due to technical difficulties.
(Why do I think there may be a more elegant solution?)
Edited on December 28, 2019, 9:34 am