While I applaud your attempt to use trigonometry in response to the Lake Ponchatrain case, you have made a significant error.  You are mixing polar and cartesian coordinate systems.

The use of geometry to determine the radius of the earth (geo - earth, merty - measurement) goes back to the ancient Greeks and peoples of the subcontinent of India.  Two historical figures whose mathematical computations estimated the radius of a spheroid earth of approximately 6370 kilometers are Eratosthnes (Greece) and Al Beruni (India).  These scholars worked independently, as they were significantly removed one from the other in space and time, and arrived at similar results using different methodologies.