Are "in a distance" and "at a distance " synonyns? Please give examples. No. "At" specifies a location, time, or position. Using "at" is similar to pointing your finger at something. You could say "I see an eagle at a short distance from that tower" and it would be like pointing your finger at the eagle that is near the tower. I can't think of many uses for "in a distance" but "in the distance" is very common. You could say "I see an eagle in the distance" and it would mean that you see an eagle far away. Here's an attempt to use "in a distance": "We're running out of gas but there is a gas station in a short distance from here" although, frankly, the word "in" would better be omitted.

Are "in a distance" and "at a distance " synonyns? Please give examples.