SOLUTION: need to find what the sides of a equilateral triangle measure on the inside of a six foot circle. and how you came about the answer

Question 4402: need to find what the sides of a equilateral triangle measure on the inside of a six foot circle. and how you came about the answer
Found 2 solutions by khwang, cleomenius:
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
The simplest way : use the sine law
a/sin A = 2R,
Here, sin 60deg = sqrt(3)/2 and R = 6.
So, a = 6 sqrt(3) ft
Kenny

Answer by cleomenius(959) (Show Source): You can put this solution on YOUR website!
Since this is an eqilateral triangle, angles are congruent (60 degrees)
My solution is as follows,
First I drew an angle bisector from one of the angles (the top angle for convenience.)
I extended this down to the center of the circle, which would be half the diameter or 3.
I drew radius as a perpendicular bisector to the angel on the left side.
So the angles formed from the triagle formed on the left are 30 degrees, and the center angle will be 120 degrees. As there are 3 of them around the center, this checks as they add to 360 degrees.
I drew a perpendicular bisector from the 120 degree angle to a side of the triangle, this forms a 30 60 90 triangle, in which we do know the value of the hypotenuse to be 3. The side opposite thr 60 degree angle is the value we are looking for. This value is s, or 3, times /2.
Since this is only half the value of the side we need, the value of the side of the triangle will be 3 times , or roughly 5.2.
Cleomenius.

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