What was the purpose for roman arches???

it was used in creating bridges and aqueducts that aids in spreading their culture across Europe and Middle East

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.