The only standard is that the top face is parallel to the bottom face - or, the table. Any ratio will satisfy this, as long as all 10 faces are identical and the die isn't asymmetrical between the two 5-edge vertices.
Since any ratio satisfies it, I'm going to use my imagination and guess that the one which maximizes the ratio of kite edges to kite area is the one which would be the most likely design standard. This optimized shape is closest to square and easiest to print a readable number into.
I'm skeptical though that there's any "standard", because I possess D10's which are designed more pointily or flatly than others. None of them are very far from the area-maximizing ideal I mentioned above, but they aren't "standardized" or identical.
I also haven't figured out how to calculate the "best" kite shape which can fit as an edge on a truncated pentagonal pyramid, but I do think that there is a "best" one and that it's best for the reason given: It results in the face with the most printable area and least sharp angles, or, looked at another way, the smallest ratio of short-sides to long-sides. Closest to square you can get without breaking the pyramid's geometry (obviously you can't get square). It might be the one which has a right angle between long faces and short faces. I haven't proved it but I'm convinced that there's only one solution to that, and that it's also the same as the solution to maximizing the area-to-circumference ratio.
Later I may improve this answer by measuring my own D10's to see if their middle vertices are very close to that right-angle figure, and maybe by developing those two proofs - which would additionally yield specific proportion figures for the whole die.