where 19,5º comes from? let's find out.
let us assume we have a tetraedr with all side of length 'a'.

the angle between the edge and middle point on top view of the tetraedr is 30º. tangent of an angle equals to opposite divided by adjacent. let opposite be 'c', and adjacent is a/2, then:
$$ \tan 30^{\circ} = \frac{c}{a/2} $$