The Golden Gate Bridge is a magnificent structure that connects the San Francisco peninsula in the north with southern Marin County, near Sausalito. Crossing the bridge costs approximately USD $8. The roadway or roadway is on a reinforced structure 3 meters high, and is suspended by two huge main cables attached to the towers, which reach a height of 230 m above sea level, the cables take the form of a parabola and touch the roadway in the center of the bridge. There are 70 m between the roadway and sea level. Its dimensions are shown in the figure below. What is the length of the cables attached to the towers, which support the bridge structure for 1280 m, and which also touch the roadway at the center of the bridge?

Calculate analytically (20 pts)