If a right triangle has one side that is 500, another side that is 208, and the last side with a radius of 705, what is the formula to determine the length of the intersection point (y) at any given value of the x axis?
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If the center of the circle is assumed vertically above the left vertex (which fits well as the difference between $(705-208)^2+500^2$ and $705^2$ is "negligibly small" $16$), then $$ y=\sqrt{705^2-250^2}-\sqrt{705^2-500^2}\approx 161.$$