Jim

This is a fun law of sines problem.  As we all know the theoretical top 
tube length is the one that tells you about fit, since it's the level 
distance from the seat tube to the head tube.  But since you asked, here's 
how you set it up:

We've got a triangle with three sides with lengths a, b and c.  It has 
three angles: A, B and C that are opposite each of the three sides.  The 
law of sines tells us that:

a/(sin A) = b/(sin B) = c/(sin C)

What this means is if you know a few of these, you can calculate the rest. 
 The triangle I'm drawing has two top tube lines that intersect at the head 
tube: a = the THEORETICAL TT, and b = the ACTUAL TT .  The third side is c 
= the short line along the seat tube that connects the two top tube sides.  

Angle C opposite line C is the slope of the actual top tube = 6 degrees
Angle B opposite the actual TT is the seat tube angle = 71.8 degrees
Angle A opposite the theoretical TT is the rest = (180 - 71.8 - 6) = 102.2 
degrees

Since we know A, B, C and a, we can plug into the law of sines and solve

a/(sin A) = b/(sin B)
b = (sin B) * a/(sin A)
b = (sin 71.8) * 57.5cm/(sin 102.2) = 55.88cm

On Friday, June 27, 2014 7:55:51 AM UTC-7, Jim Bronson wrote:
>
> What's the (non-theoretical) TT on this frame?  The TT listed on the 
> Rivendell geometry charts is theoretical.
>
>
>

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