Who initially controlled the roman republic

The final defeat of Mark Antony and his ally Cleopatra at the Battle of Actium in 31 BC, and the Senate's grant of extraordinary powers to Octavian as Augustus in 27 BC – which effectively made him the first Roman emperor – thus ended the Republic.

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.