SOLUTION: Find the perimeter of an equilateral triangle that can be inscribed in a circle whose circumference is 50 meters.

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Question 1014340: Find the perimeter of an equilateral triangle that can be inscribed in a circle whose circumference is 50 meters.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So the radius of the circle is,
2pi%2AR=50
R=25%2Fpi
The equilateral triangle inscribed in the circle is made up of 3 isosceles triangles that have 2 sides equal to the radius of the circle and the third side equal to the length of the side of the equilateral triangle.
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From trigonometry,
cos%2830%29=%28S%2F2%29%2FR
S=2Rcos%2830%29
For an equlateral triangle,
P=3S
P=6Rcos%2830%29
P=6%2825%2Fpi%29%28sqrt%283%29%2F2%29
P=%2875sqrt%283%29%29%2Fpi%29
highlight%28P=%2875sqrt%283%29%29%2Fpi%29%29