What is the distance on the ground between 2 posts when the posts are attached to a platform that is 6 feet square and attached with 15 degree brackets? The posts are either 10 foot or 12 foot. Please answer for both.

If you mean the posts make a 15° angle with the vertical, and slope outwards from the corners of the platform, in line with the sides (see how specific you need to be?) then for 10' posts the distance d is

d = 6 + 2(10 sin15°)