I don't get 59.9 from that calculation; but I did get 59.9997 from the correct calculation. You didn't really want to use cos(63), did you? (That would be for longitude.)
Assuming you really did the correct calculation, your problem is just that you are not finished. That is the number of degrees AWAY from the given point, not its latitude!
OK I did the formula for an arc of longitude instead,
l=C*(a)/360
6702.9=40217.6*(a)/360
(a) = (6702.9*360)/40217.6
(a) = 59.9997 degrees
Now I have to either add or subtract this value from 63 degrees, because it's the latitude that is given would be the sector angle no?
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