Whoops! Well... Estonian isn't exactly distantly related, as it's quite close... but my mistake nonetheless. Turkish isn't considered to be related at all here, here's a few sentences from SoG's post that support this:
The Ural-Altaic language family is an hypothetical grouping of the Uralic and Altaic language families into one field.
The Ural-Altaic grouping is speculative, as it has not been proven to the satisfaction of most linguists that there is any genetic relationship between the two language families, and even the existence of the Altaic group as one family is today questioned.
Most modern linguists argue that Uralic and Altaic have not been shown to bear any exclusive genetic relation
Uralic and Altaic are no more closely related to each other than either of them is related to any of this macrofamily's other members, e.g. Uralic with Indo-European or Altaic with Indo-European.
Finnish is a part of the Uralic languages, while Turkish belongs to the Altaic language family.