# Just hangin' around ......

Suppose there are two (vertical) poles, one of height $$100$$ feet and the other $$70$$ feet, positioned a horizontal distance of $$80$$ feet apart on level ground. A rope of length $$100$$ feet connects the tops of the two poles. A weight, placed on the rope so that it can slide freely along it, is allowed to come to rest.

Once at rest, the weight is a horizontal distance $$X$$ from the $$100$$ foot pole and a vertical distance $$Y$$ above the ground. Find $$X + Y$$.

Clarification: Assume that the rope forms a straight line from the weight to each of the pole tops.

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