Question

Distance from centroid of an equilateral triangle to one of its corners

Answer 1

let's assume each side=x
then from one corner to point which bisects opposite side=
$\sqrt{ {x}^{2} - { \ \frac {x}{2} }^{2} }$
=
$\sqrt{3} \frac{x}{2}$
so distance of centre from one corner=(2/3)×(sqrt(3)×(x/2))=x/(sqrt3)

Answer 2

The distance of the corner is
$a \div \sqrt{3}$