tramp-remote-path

tramp-remote-path is a variable defined in `tramp-sh.el'.
Its value is

(tramp-default-remote-path "/bin" "/usr/bin" "/sbin" "/usr/sbin" "/usr/local/bin" "/usr/local/sbin" "/local/bin" "/local/freeware/bin" "/local/gnu/bin" "/usr/freeware/bin" "/usr/pkg/bin" "/usr/contrib/bin" "/opt/bin" "/opt/sbin" "/opt/local/bin")

Documentation:
List of directories to search for executables on remote host.
For every remote host, this variable will be set buffer local,
keeping the list of existing directories on that host.

You can use `~' in this list, but when searching for a shell which groks
tilde expansion, all directory names starting with `~' will be ignored.

`Default Directories' represent the list of directories given by
the command "getconf PATH". It is recommended to use this
entry on top of this list, because these are the default
directories for POSIX compatible commands. On remote hosts which
do not offer the getconf command (like cygwin), the value
"/bin:/usr/bin" is used instead of.

`Private Directories' are the settings of the $PATH environment,
as given in your `~/.profile'.

You can customize this variable.