Q&A #6322

Teachers' Lounge Discussion: Measuring arc length

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From: Philip Wetherington <philva@mindspring.com>
To: Teacher2Teacher Public Discussion
Date: 2004030821:02:12
Subject: Finding the radius of a circle when you only have an arc

I have a board that is 6 inches wide and 20 inches long. I want to cut
an arc in the board that starts at the lower left bottom corner of the
board and runs to the lower right corner of the board. In the middle
of the board the height of the arc will be 4 inches from the bottom of
the board (midpoint along the bottom of the board). If I know the
formula for this, I can mark the point 4 inches up from the midpoint
at the bottom of the board, run down the radius line the "proper
distance",(this is the unknown I'm looking for), anchor the end of a
string, run back up the distance of the radius, wrap the string around
a pencil and draw my arc.
This is not a hypothetical question. I am a woodworker and find myself
having to construct such an arc quite often using a time consuming
"trial and error" method. A formula using the 22 inches and 4 inches
to find the center of the circle, and thus the radius would be a

Thank you for your help,  

Philip R. Wetherington
Macon, GA

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