Name: nancy
Who is asking: Student
Level: Secondary

Hi, I donāt understand this problem, could you possibly solve and explain it to me? Just assume there is exactly one half acre of grazing area for the goat:

A farmer has a fenced-in, circular field with an area of about one acre. A goat in the field is tethered to one of the fence posts with a rope which gives the goat approximately one-half acre of grazing area. To the nearest foot, how long is the rope?

Thank you so much!!!!

Hi Nancy,

This is quite an old problem. It seems to have first appeared in the first volume of the American Mathematical Monthly in 1894. The solution involves trigonometry and then approximating the solution to a trigonometric equation. I am not going to reproduce the proof here but you can find it in the Mathematics Magazine, Volume 55, Number 4, 1982 pages 221 to 227. Mathematics Magazine is published by The American Mathematical Association.

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