Truing a 30-60-90 Triangle

In many instances, cutting dovetailed open mortises through a Roubo bench top for example, a 30-60-90 layout gauge only has to be “close enough,” however you define that term.  All one layout line has to do is match another layout line, and as long the two lines are struck with the same tool off the same reference plane all is well.

During last year’s workshop we all made one or two of these triangles, and like I said above, they work just fine.  Laying out the hypotenuse with dividers was all that really needed to accomplish (the hypotenuse of a 30-60-90 triangle is exactly twice the length of the short leg), using my Chris Vesper sublime refence square for the 90-degree corner.

But what happens when you have to create a series of lines coming from different places, and they establish the perimeters of pieces that must match each other precisely?  That is exactly the case of laying out a basic “starburst” or “dice” pattern parquetry composition.  I used to be content with simply laying out a sawing jig using a small plastic triangle from a middle school geometry class set, but since I have moved to shooting the edges of all the lozenges to minimize the joints even more, I needed to make myself a truly precise triangle square to set the fence for the shooting board.

Starting with one of the brass triangles left over from the workshop two summer ago I determined to make a 30-60-90 square that fit the bill.  Once I had the angles perfect I could then solder on the shoe to the short leg of the triangle.

Tomorrow I will show how I did just that with a bench top geometry version of a Covid/PCR test, using a piece of paper and two popsicle sticks.