document.write( "Question 759127: Please help me figure out the side length of an equilateral triangle inscribed in a circle with the radius of 21 \n" ); document.write( "

Algebra.Com's Answer #461956 by Cromlix(4381) $\"\"$ $\"About$

You can put this solution on YOUR website!
With the equilateral inscribed in the circle
\n" ); document.write( "draw one of your radii from a vertex to the centre.
\n" ); document.write( "Then take another radii from another vertex to the centre.
\n" ); document.write( "You now have a triangle with 30 degrees at the points
\n" ); document.write( "touching the vertices and 120 degrees at the centre.
\n" ); document.write( "Mark the triangle with A at the centre and B and C
\n" ); document.write( "at the vertices.
\n" ); document.write( "Use Cosine Rule.
\n" ); document.write( "a^2 = b^2 + c^2 - 2bc CosA
\n" ); document.write( "a^2 = 21^2 + 21^2 - 2*21*21*Cos 120 degs
\n" ); document.write( "a^2 = 1323
\n" ); document.write( "a = square root of 1323
\n" ); document.write( "a = 36.4 units.
\n" ); document.write( "Hope this helps.
\n" ); document.write( ":-) \n" ); document.write( "

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