SOLUTION: A circle is 20 meters across the radius, and we want to fence the circumference at 2 meters per piece, how many fence pieces will I need for the circle.

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Question 817147: A circle is 20 meters across the radius, and we want to fence the circumference at 2 meters per piece, how many fence pieces will I need for the circle.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You have the circle cut into sectors with two sides 20 meters and one side 2 meters in length. The circumference of the circle is 2*pi*20, but because the fence pieces form chords, the length of each fence piece is somewhat less than the corresponding arc of the circle sector. You want to find the value of each central angle where the radii meet. First, examine the isosceles triangles.

Each isosceles triangle is made of two right triangles, one leg being 1 meter and the hypotenuse being 20 meters. Draw the circle and these two triangles to see this. Sin%28a%29=1%2F20 where 2a is the value of the central angle.
'
a=arcsin%281%2F20%29
2a=2%2Aarcsin%281%2F20%29

Now, how many of these 2a degrees are in 360 degrees?
highlight%28360%2F%282%2Aarcsin%281%2F20%29%29%29