Gene,
Check your in box.
I sent you the answer to your question in the form of a jpeg drawing 
for both the internal thread and the external thread.
You can't just use the trig for an equilateral triangle because real 
threads are not equilateral triangles but are really trapezoids with 
flattened 60 degree included sides but with flattened tops and bottoms.

for a class 3B fit (tight maybe needing a wrench) the height of an 
internal thread is P x .54127  or .54127 / tpi
  and the height of an external thread is .6134 x P or .6134 / tpi

I would post the jpegs but don't have a site to do that on.  You are 
welcome to post them to your site if you desire.

Cecil


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