I have two commit shas and I want to know if the first is an ancestor of the second. Put another way, is this first commit somewhere in the history of this other commit.

Git's merge-base command combined with the --is-ancestor flag makes answering this question easy. Furthermore, because it is a plumbing command, it can be used in a script or sequence of commands as a switch based on the answer.

Here is an example of this command in action:

$ git merge-base --is-ancestor head~ head && echo 'yes, it is'
yes, it is
$ git merge-base --is-ancestor head~ head~~ && echo 'yes, it is'

In the first command, head~ is clearly an ancestor of head, so the echo command is triggered. In the second, head~ is not an ancestor of head~~ so the return status of 1 short-circuits the rest of the command. Hence, no echo.

See man git-merge-base for more details.

source