SOLUTION: A goat is tethered to the outside corner of a 10m by 10m square enclosure by a 15m long rope. What area can the goat graze? (Assume the goat cannot jump into the enclosure.)

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Question 712653: A goat is tethered to the outside corner of a 10m by 10m square enclosure by a 15m long rope. What area can the goat graze? (Assume the goat cannot jump into the enclosure.)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The goat can pull the rope straight, adjascent to one side of the corner, and can move at that distance from the corner to pulling the rope adjascent to the other side of the corner, covering 270 degrees of a circle with radius 15 feet, the length of the rope.

The area is %28270%2F360%29%2Api%2A15%5E2 feet^2

The goat while at either side with rope against that side, can move 1/4 of a circle at radius 15-10=5 feet. There are two of these, one for each side of the corner at which the goat is tethered.

These two smaller parts are 2%2A%2890%2F360%29%2Api%2A5%5E2 feet^2

The sum of all of these areas is highlight%28%28270%2F360%29%2Api%2A15%5E2%2B2%2A%2890%2F360%29%2Api%2A5%5E2%29 ft.^2