Question 568999
{{{drawing(300,240,-12,6,-1.5,13.5,
triangle(-10,0,-10,12,0,4),
triangle(0,4,5,0,5,6),
line(0,0,0,4), line(-12,0,6,0),
locate(-10.2,0,A), locate(-0.2,0,F),locate(4.8,0,E),
locate(-10.2,13,B), locate(-0.2,5,C),locate(4.8,7,D)
)}}} AB and ED are the poles (perfectly vertical). BE and DA are the ropes that cross at C.
F is the point directly below C on the ground (line AE), which is pefrectly flat and horizontal.
The vertical poles are part of parallel lines.
As a consequence, triangles ABC and DEC have congruent angles at B and E, and at A and D (alternate interior). Of course, ABC and DEC also have congruent angles at C (vertical angles).
Triangles ABC and DEC are similar, with corresponding sides in the ratio 2:1
{{{AB/DE=BC/EC=AC/DC=2/1}}}
In particular,
{{{BC=2EC}}} and {{{BE=BC+EC=2EC+EC=3EC}}}
Right triangles ABE and FCE, with the same angle at E, are also similar, so
{{{AB/FC=BE/CE=3EC/EC3/1}}} --> {{{AB=3FC}}} --> {{{FC=AB/3=12ft/3=highlight(4ft)}}}
The ropes cross 4 ft above the ground.