Goat

Meadow is a circle with radius r = 19 m. How long must a rope to tie a goat to the pin on the perimeter of the meadow to allow goat eat half of meadow?

Correct result:

x =  22.02 m

Solution:

S1+S2=12S S=πr2 S1=12x2(αsinα) S2=12r2((2π2α)sin(2π2α))  x=2rcos(α/2)   α=tanαπ2cosα    x=1.158728419=22.02 m



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