Meaning of the symbols:
(See diagram on progam page.)

r₁ is the length of the line between Points P1 and P2.
r₂ is the length of the line between P2 and P3.
h1 is the length of the line between P2 and P4.
h1 is the length of the line between P4 and P3.
Rz is the length of the line bewteen P1 and P3.
α is the proportion of the length of Rz that h1 is.

The aim is to calculate α if only r1, r2 and Rz are known.

This equation does that.

The program tests the equation, by creating points/lines you specify the co-ordinates of, then calculating r1, r2 and Rz for
those lines, using the equation to calculate α, which should
then correspond totally accurately to the position
on line Rz corresponding to the x co-ordinate of P2,
so we can see if the equation is correct or not.

The program draws the position of α as an indicator line
in orange below the x-axis.

See also the calculation output text for the actual numbers.

 

 

 

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