Collocations for distant - adj.

be, sound
become, grow
The sound of the engine was growing more and more distant.

extremely, fairly, very, etc.
far (literary)
in far distant lands

relatively
increasingly
geographically, physically
geographically distant areas of the world

from
The stars are more distant from the earth than the sun.

two miles distant, three days distant, etc.
These sites were often several miles distant from each other.

be

impossibly
The medieval mind can seem impossibly distant.

historically

in the far distant future
in the not too distant future, in the not too distant past
In the not too distant future, we may witness the cloning of human beings.

the dim and distant past (BrE)
stories from the dim and distant past

be, feel, look, seem, sound
He felt oddly distant from her.

become, grow
remain
find sb

extremely, fairly, very, etc.
increasingly
Their relationship has grown increasingly distant in recent years.

a little, slightly, etc.
oddly, strangely
Even his children found him strangely distant and impersonal.

emotionally

cold and distant
When they met, he was very cold and distant.

Distant is used with these nouns:
ancestor, bell, corner, country, cousin, descendant, dream, drone, echo, explosion, father, future, galaxy, gleam, gunfire, hill, hillside, hope, horizon, kin, land, look, memory, mountain, murmur, object, past, peak, planet, relation, relationship, relative, roar, rumble, shore, shout, siren, sound, star, thunder, voice, wail