A goat is tied to a long straigh wall by a rope.
The ends of the rope are tied to two hooks secured in the wall and the rope can slide through the ring attached to the goats collar.
The hooks are separated by 40 feet and the rope is 50 feet long
The ends of the rope are tied to two hooks secured in the wall and the rope can slide through the ring attached to the goats collar.
The hooks are separated by 40 feet and the rope is 50 feet long
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This is going to be an elipse, assuming that the rope doesn't get snagged when the goat moves to the other side of the wall. The major axis of the elipse is 50 feet; the foci are at the hooks.
The area available for grazing is Pi r1 r2 = Pi (25 feet) (15 feet) = 375 Pi ft^2.
If the rope can't go through the wall, then the shape is a half-elipse with two semicircles attached to it of radius 5, for a total area of 375/2 Pi + 25 Pi = 212.5 Pi ft^2
The area available for grazing is Pi r1 r2 = Pi (25 feet) (15 feet) = 375 Pi ft^2.
If the rope can't go through the wall, then the shape is a half-elipse with two semicircles attached to it of radius 5, for a total area of 375/2 Pi + 25 Pi = 212.5 Pi ft^2