Make a template using a string and a pencil. Cut the string to the correct length, place the pencil point at the center of the arc (or circle since an arc is only a portion of a circle) and draw 48".
I don't that will work: the piece seems to be a curved member (What radius?) whose LENGTH along the outside of the arc is 48".
So, with a string and pencil, or thin board (1/2 x 1/2, 1 x 1/4) with a pencil hole in one end, and a pointer hole in the other (???) distance away, draw a circle. Take the string or tape measure, or one inch long strip of wood, or rule exactly one inch wide, and mark off 48 increments along the circle.
A little faster, but a little less accurate? Use a 2" or 3" strip. Get one of those cheap ($1.50) little compass sets from the grocery store and use it to mark off equal lengths.
For what you are cutting (Shaker furniture), this method of using a bunch of small straight lengths around the circle will be accurate enough.