I cheated. It has been far too many years since I took trig. I found this calculator:
I started with the formula Arc Length = degrees X ((PI X Radius)/180). I changed this to
degrees = Arc Length X (180/(PI X R)). This gave me an angle of 9.671342 degree. Using
the calculator above I entered sides a & c as 1517.15 and the angle between these
sides as 9.671342, selected side b as the value to find and clicked the "calculate
selected" button. It calculated side b to be 255.7861.
Either my 255.7861 or your 254.88 wouldn't make much difference.
Jim Barrett - Timpson, TX
From: Jeff Owens <owensj(a)epix.net>
Sent: Wednesday, April 30, 2014 9:25 AM
Subject: Re: [DMU] Entering an Arc
It is a pretty gradual curve. For cross checking purposes using Jim's
suggestion the straight line length (the chord distance for that arc)
calculates to 254.88 feet using two place round off. Ck my math haven't
calculated one of these in years.
/r/ is the radius of the circle
/c/ is the angle subtended <http://www.mathopenref.com/subtend.html>
the center by the chord (9.67 deg by my calculation --- 256.09 divided
by 9532.52 times 360 )
/sin/ is the sine function (c/2 = 4.835 and sine of which is ~.084)
2 x 1517.15 x .084 = 254.88
Must be a pretty recent survey. This calculates to a difference of two
feet difference at the center of the arc. I can't imagine old timers
worrying about 2 feet one way or the other as far as how it affects the
right of way of the road. When curbs and sidewalks; utility placement
are concerned in today's world, I suppose it matters.