The centroid of ABC is G. Find AG.
This is an isosceles triangle
The height = the length of the median drawn from A
Using the Pythagorean Theorem .....Height = sqrt [ 8^2 - 1^2 ] = sqrt 63 = 3sqrt 7
AG = (2/3) Height = (2/3) * 3 sqrt 7 = 2 sqrt 7