How the US gain the rights to the Panama Canal zone? Why did they want it

The Hay-Bunau-Varilla Treaty signed, granting the United States a strip of land across the Isthmus of Panama and the right to build and fortify the Panama Canal.

"The Americans knew they needed this to move ships from east to west quickly. If they did that, they would control power because they would control the oceans. The Canal was a geopolitical strategy to make the United States the most powerful nation on earth."

The U.S acquired the 'Panama Canal' project from the French for $40 million. canal would shorten the journey for both European and US merchant ships travelling east from the Californian coast.

Explanation:

answer: this problem has only trivial solutions, with all points on the same line. x=5 or x=7/5.

step-by-step explanation:

there are three triangles, and three unknowns: x, y=length of middle segment, and z=cos(angles marked with red arc).

we need

and law of cosines,

the three equations are

see attached image for solution.