What is the size of the largest square which can fit inside a regular pentagon with a side-length of 1?
Assuming the best orientation is with one side of the square parallel to one side of the pentagon the side length can be found using the law of sines on a couple of triangles formed.
The side comes out to be sin(108)/(sin(36)+sin(18))
=√5 - .5√(10-2√5) ≈ 1.0605
Posted by Jer
on 2013-12-02 15:58:05