circle packing – trigonometry- Construction Profession needs help

Architect designed floor layout with a radius that is outside of the building and too far away to see the vertex. Normally we would pull a string the length of the radius but that is not an option. Is there a way to calculate the height of an arc from different points along the chord?

Example- I know where the arc starts and ends, the radius is 300′ and not visible from inside the building but we also know the chord length is 50′. How can I plot the curve of this circle every 3′?
The intention is to draw the arc on the floor as close as possible.