SOLUTION: Two vertical poles have heights 6 ft. and 12 ft. A rope is stretched from the top of each poles to the bottom of the other. How far above the ground do the ropes cross? *Note: I

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Question 568999: Two vertical poles have heights 6 ft. and 12 ft. A rope is stretched from the top of each poles to the bottom of the other. How far above the ground do the ropes cross?
*Note: I need to solve this problem using similar triangles.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
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%2FDE=BC%2FEC=AC%2FDC=2%2F1
In particular,
BC=2EC and BE=BC%2BEC=2EC%2BEC=3EC
Right triangles ABE and FCE, with the same angle at E, are also similar, so
AB%2FFC=BE%2FCE=3EC%2FEC3%2F1 --> AB=3FC --> FC=AB%2F3=12ft%2F3=highlight%284ft%29
The ropes cross 4 ft above the ground.