The 30-60-90 Challenge

Goal:  Draw a 30 and 60 degree angle using only a framing square.  Twelve sided columns were used in many historical homes.  How did carpenters then (and now) use the framing square to create the needed angles of 30 and 60 degrees?

Materials allowed:  Paper, pencil, framing square, and your knowledge about the ratios of the sides in a 30-60 right triangle.

Hint:  Draw a line 16” long (or any length you wish).  Use this as a hypotenuse of the framing square.


  • Ryan
    Posted at 17:51h, 12 February Reply

    What is the answer to this problem?

    • Geometry in Construction
      Posted at 21:10h, 18 February Reply

      Draw any length line….let’s say a 16 inch. Using what we know about the 30-60-90 relationships…..the short leg is half the length of the hypotenuse….using a framing square to draw the 2 legs (perpendicular to each other which is what the right angle part of the framing square does), let one leg be an 8 inch length (half of the 16 inch) and the other leg be whatever length it needs to be to complete the right triangle. You have now created a triangle with a 30 and 60 degree angle.

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