When using tangent to measure a tree from different distances will your answers vary a bit?

The answer would vary a bit because of calculation error.  Whenever you do any 'experiment'  there is always going to be a little bit of variation in the output.  However, if you do it properly, there will be NO SIGNIFICANT DIFFERENCE.

does that make sense?

Nope.......the distance will change, but so will the angle of elevation.........also, if the tangent only "worked" at certain distances, it would be largely useless.

Think of it this way......suppose we could tie a string to the top of the tree and anchor the other end of it in the ground some distance from the tree. Now, move the anchor point closer to the tree. The angle of elevation is different, but the height of the tree is the same. The angle of elevation would decrease if we moved the anchor point away from the tree, but again, the tree's height would be the same.