"Gramp's shop" wrote:

I need to draw an arc for a piece of trim. The end points of the arc are 5 feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to trial and error, oui?

Larry

No trig or anything real advanced needed here. Merely that the square
of the hypotenuse of a right triangle = the sum of the squares of the
other two sides

Picture your arc, and a line between the ends of the arc. Now draw
another line from the center of your circle to the midpoint of the
arc, and a third line from the circle center to one of the endpoints.
Now if you have a circle of radius R, you have just drawn a right
triangle with hypotenuse R, one side of R-2, and the other side of 30
(converting the 5-ft width to inches and dividing by 2.

30^2 + (R-2)^2 = R^2

900 + R^2 -4R + 4 = R^2

904 = 4R

R=226"
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