Question

The figure below shows a regular hexagon inscribed in a circle. The length of each side of this figure is 8 cm. Which of the following values represents the length of apothem PQ?

Answer 1

The answer is 4√3 or 6.3

Answer 2

The size of angles in a hexagon is:
[(n-2)*180]/6
=(720)/6
=120°

thus the length of the apothem will be found as follows:
tan θ=opposite/adjacent
θ=120/2=60
opposite=apothem,a
adajcent=base=8/2=4
hence
tan 60=a/4
a=4 tan 60
a=6.93
Thus PQ=6.93