How far from the ground do the ropes cross? In ft.

Question

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

Answer 1

Assume the distance between the to poles is "d".

Assume the horizontal distance of the intersection from the 6 ft pole is "a".

Assume the horizontal distance of the intersection from the 12 ft pole is "b".

Assume the distance of the intersection above the ground is "y".

By similar triangles y / 6 = b / d → y = 6b / d

By similar triangles y / 12 = a / d → y = 12a / d

The above results in 2a = b

The point of intersection is 1/3 of the distance from the 6 ft pole to the 12 ft pole.

The point of intersection is 6b / d or 12a / d.

Answer 2

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