How would one figure the length of an arc that chord is 16 feet long
and a vertical line from the center of the chord to the arc raises 4
feet?

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Request for Question Clarification by mathtalk-ga on 11 Nov 2004 13:34 PST

Hi, latheid-ga:

If the Comment below satisfactorily answers your Question, I would not
want to post an Answer that you'll be charged for.  However if you
want a more "formula-driven approach" to use fractl-ga's expression,
let us know.

fractl-ga is correct that the radius of the circle is 10 feet. 
However an error crept into calculating the final number by using
pi*r^2 (area) instead of 2pi*r (circumference).  The length of the arc
is ~ 18.546 feet.

regards, mathtalk-ga

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Clarification of Question by latheid-ga on 12 Nov 2004 04:23 PST

The information provide is enough. Thanks

not the most formula-driven approach, but its most likely the easiest...

imagine the entire circle with a 16 ft cord running from pt A to pt B.
 consider the center of the circle as M and the midpoint of chord AB
as T.  note that this point T is where the 4ft perpendicular line is
raised.

I used the right triangle BMT to find the radius of the circle.  BT is
8 (half of 16) BM is r (the radius) and TM is r-4.  this gives the
pythagorean equation (r-4)^2+8^2=r^2...solving this shows that the
radius is 10 ft.

from there you can get the angle of BMT in the 6-8-10 triangle by
finding the sin^-1(8/10) = 53.13 deg.  The size of the angle BMA is
therefore 2*53.13 or 106.26.  take the total circumferance
(pi*10^2)=314.15 and multiply by 106.26/360 to get 92.7295 as the
length

I hope this helps you


I am not a Google Researcher, I just don't have anything better to do :P