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How do you calculate arc length given length of chord and distance of chord to arc through the center?
Wiki User
∙ 12y ago
It is much easier to follow what is below if you have a rough sketch.
Suppose the length of the chord is 2x units so that half the chord is x units.
Suppose that the distance from the centre of the circle to the arc = y units.
Suppose the angle subtended at the centre by the chord is 2k radians.
Then the semi-chord and the line from the centre form a right angled triangle with the radius to the end of the chord, and the angle subtended by the semi-chord at the centre is k radians.
Now, by Pythagoras the radius, r = sqrt(x2 + y2) units
and tan(k) = x/y (or sin(k) = x/r
Since both x and y are given, r and k can be calculated.
Then arc length = r*k which is a simple multiplication.
If you measure angles in degrees, remember that pi radians = 180 degrees.
Wiki User
∙ 12y ago
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