If you are talking about two friends and you've already described one of them, then there's one friend left to describe: the. "Another" would mean there are more friends in your room, but you haven't really specified which friend is how tall.

If you are talking about 2 people you know... you will have to use other in this case..

"another" means different here you have the situation where you are talking about a certain "similarity" which is their height

Using another would seem to suggest that there are more than two friends in your room. With only two friends, you have one and the other. With three friends in the room you might have heights for one and another of the other two friends. I hope that makes sense.