Heptagonal Triangle and Trigonometric Identities,
Forum Geometricorum, 19 (2019) 29-38.
Abstract. We will study the trigonometric identities for heptagonal triangles.
Let a < b < c be the heptagonal triangle’s sides and let R be the circumradius. We will prove the following:
2b^2 – a^2 = √7bR, 2c^2 – b^2= √7cR, 2a^2 – c^2 = −√7aR.
We will also prove the following trigonometric formula:
4 sin 2kπ/7 – tan kπ/7 = √7for k = 1,2, 4 and -√7 for k = 3,5,6.