A regular decagon is inscribed in a circle of radius 11 m Fi

A regular decagon is inscribed in a circle of radius 11 m. Find the length of a side of the decagon. One of the sides of the decagon is meters. (Round to the nearest tenth as needed.)

Solution

Law of Cosines applies to any triangle and relates the three side lengths and a single angle

c^2= a^2 +b^2 - 2abcosC

In the case of our regular n-gon, we have a = b = r and C = 360°/n, so we simplify it to

c^2 = r^2 +r^2 - 2r^2cosC

= 2r^2( 1 - cos(360/10))

= 2*121(1 - cos36)

= 242(1 - cos36) = 46.217

c = 6.79 = 6.80 mt