METAPOST -- specifying an unknown point coordinate by giving the angle from another known point

[James Fisher <jameshfisher@gmail.com>]

This isn't specifically a ConTeXt question, but via it I've run into a
seemingly simple problem in METAPOST that I just can't solve.  I'm
trying to draw a parallelogram by specifying: (1) the length of sides
parallel to the x-axis; (2) the total height of the figure; (3) one of
the interior angles.  This is how I'm trying to solve it:

-----------------

% Draw a parallelogram, like so:
%
%         z3    z2
%         +-----+   ^
%        /     /    |
%       /     /     |
%      /     /      |10 units
%     /BL   /       |
%    +-----+        v
%   z0     z1
%    <----->
%    5 units
%
%    Interior angle BL = 87 degrees


beginfig(1);

  z0 = origin;        % bottom left
  z1 = (5,0);         % bottom right
  y2 = y3 = 10;       % shape is 10 units high
  x2 - x3 = x1 - x0;  % top edge is the same length as bottom edge

  % We've completely specified z0 and z1;
  % We know that the top edge is the same length and angle as the
bottom, but lies somewhere on y = 10;
  % all we have to do is specify one angle and we have a complete parallelogram.
  %
  % The following should work as it provides the following information:
  % the unit vector from z0 to z3 is at an angle 87 degrees
anticlockwise from (0,0) -- (1,0).

  angle(z3-z0) = dir(87);

endfig;
end;

--------------------

This doesn't work; using the angle() function gives the error:

   Not implemented: angle(unknown pair).

Strictly speaking, yes, z3 has an unknown x-coordinate at that time in
execution.  But I am told that METAPOST is declarative, so I would
expect my line of code to mean: "set the x-coordinate of z3 such that
angle(z3-z0) = dir(87)".  AFAICS that provides all the needed
information to draw the shape.

So, is there another way I can do what I want without falling into
low-level trig?



Best,


James
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