Ok. So my envelope drawing I'll try to explain:

13' away and 60" (diagonal vs height shouldn't matter nor should units since it's all ratios) gives a ratio of 60/13 = 4.61

For 15.5'
x/15.5 = 4.61
x=71.5"

So a diagonal of 71.5" at 15.5 feet should be equivalent to 60" at 13 feet.

I think it's that simple. 71.5" seems like about the right number too.