i have a problem working out the correct arch under a queenslander house 3 metres in the air

The span etween the pillers is 3280mm

So the cord is 3280mm and from the center of the cord to the radius is 450mm

I have worked the radius out to be 5238mm

Since the house is only 3000mm of the ground the center of the arc is aprox 2000mm below ground so i wont be able to pivot a string on the ground to scribe the arc on the pickets so i can cut them to the correct lenght.

I need a formula caculating the base of a triangle and scribing an arc with the apex of the triangle

ie:

A nail at the base of each piller with a piece of string around both nails up to the apex touching the middle picket. With a pencil placed at the apex in the string scribing an arc of a circle with a radius of 5238mm. what would the size of the base of the triangle have to be?

As i have about 10 arches to do all of varrying size