SOLUTION: Please solve this word problem: "A goat is enclosed in a 2(3.14) acre fenced area on the shape of an equilateral trianlgle. It is tethered to a post at one of the trianl

Question 22494: Please solve this word problem:
"A goat is enclosed in a 2(3.14) acre fenced area on the shape of an equilateral trianlgle. It is tethered to a post at one of the trianlgle's vertices. To the nearest foot, determine the length of a rope which will allow the goat to eat only one half of the grass in these 2(3.14) acres."
I have tried to solve this problem using A=bh/2 but then I get stuck on the problem. Thank you for your help.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Draw the equilateral triangle.
Each angle is 60 degrees or 1/6 th of a circle.
The area of a complete circle is (pi)(radius)^2
You want your goat to eat a swath that is (1/6)(pi)(r^2)
and for that swath to equal (1/2)[2(3.14)]
Equation:
(1/6)(pi)(r^2)= (1/2)[2(3.14)]
3.14 is approximately equal to pi so divide both sides by pi
(1/6)r^2 = (1/2)(2)
r^2 = 6
r = sqrt6 =2.44 ft.
Cheers,
Stan H.
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