I have a triangle △ABC and I know two angles of it α = 61° and β = 62° (thus γ = 180-61-62 = 57°).
How do you find a centroid of a triangle based on these fatcs only? Possibly length of one or two sides of the triangle is required for an actual value. In case let us denote them as x (and y if needed).
I assume that the side connecting angles $\alpha$ and $\beta$ is x.
By sine law, the rest of the sides can be found in terms of x. Let the side opposing the $\alpha$ be f(x).
From the triangle [$x/2, 62^0$, and f(x)], applying cosine law to it to find t (which is also in terms of x).
The centroid is located at one-third of t.