Re: draw elongated diamond

[Brian Barker <b....@btinternet.com>]

At 17:56 03/03/2016 +1100, Keith Bainbridge wrote (privately):
>On 28 February 2016 at 16:48, Brian Barker wrote:
>>At 19:19 27/02/2016 +1100, Keith Bainbridge wrote:
>>>I'm trying to draw a diamond shape with 2 opposing angles equal, 
>>>one angle 72 degrees and its opposite 60 degrees. I figured I 
>>>should be able to stretch a standard supplied shape, but can't 
>>>figure how to hold the plane of the equal angles so that the 
>>>distances from the points will vary. Then how to know that I have 
>>>72 degrees. Any pointers please?
>>
>>The internal angles of any quadrilateral must add up to 360 
>>degrees. You appear to have two lots of 72 degrees and two of 60 
>>degrees - leaving you 96 degrees short. Color me more confused.
>
>Sorry for the confusion.
>The internal angles as I walk around the rhombus will be 72, 114, 
>60, 114 degrees.

That won't be a rhombus, then - which needs to be equilateral - but a kite.

Here's an idea:

The shape you want is two isosceles triangles joined at their bases. 
The 72-degree end has other internal angles of 54 degrees. The 
60-degree end is an equilateral triangle (which is a special case of 
isosceles, of course).

o Click the drop-down (-up?) menu next to the Basic Shapes icon in 
the Drawing toolbar and then Isosceles Triangle.
o Drag to create a triangle.
o Using Position and Size..., set the width to some suitable value, say 100 mm.
o Applying the sine rule to the 72-degree triangle, its height needs 
to be 50 x sin(54 deg.) / sin (36 deg.) so set the height to 68.82 mm.
o Repeat the process to create a second isosceles triangle.
o Using Position and Size..., set rotation angle to 180 degrees, so 
as to invert it.
o Using Position and Size..., set the width to the same 100 mm as before.
o Applying Pythagoras's Theorem to this equilateral triangle, its 
height needs to be 50 x sqrt(3) mm, so set the height to 86.60 mm.
o Now move the two triangles together. You can move them using the 
arrow keys and Alt+arrow for finer control, Probably more sensibly, 
you can set the Y-positions of both shapes to be the same, whilst 
choosing different base points (one top, the other bottom) for the two.
o Click one shape and Alt+click the other, so that the combination is selected.
o Go to right-click | Group to combine the two shapes into one.
o Use right-click | Line... to set the line style to none, to remove 
the tell-tale common boundary.

You can easily move, rescale, and rotate the shape as required, of course.

I trust this helps.

Brian Barker


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