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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