document.write( "Question 1195137: Find the area of the largest equilateral triangle that can be inscribed in a circle whose diameter is
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Algebra.Com's Answer #827516 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "            How the problem is worded, it shows that its composer has
\n" ); document.write( "             $\"highlight%28quite%29\"$ $\"highlight%28low%29\"$ $\"highlight%28mathematical%29\"$ $\"highlight%28qualification%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "            The correct formulation SHOULD NOT speak about the largest equilateral triangle\r
\n" ); document.write( "\n" ); document.write( "            that can be inscribed in a circle of a given radius, because all such triangles are congruent\r
\n" ); document.write( "\n" ); document.write( "            and have the same area - - - there is NO the \" largest \" such a triangle.\r
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\n" ); document.write( "\n" ); document.write( "So, I will solve the problem in that UNIQUE (modified) formulation which is correct :\r
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document.write( "    Find the area of an  equilateral triangle  \r\n" );
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document.write( "The sine law theorem says that if any triangle is inscribed in a circle of a radius R, then\r\n" );
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document.write( "     = 2R,\r\n" );
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document.write( "where \"a\" is any of the three sides of the triangle and    is an opposite angle.\r\n" );
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document.write( "In our case, all the angles of the equilateral triangle have the same measure of 60°, so\r\n" );
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document.write( "     = 2*10,\r\n" );
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document.write( "(R = 10 cm is the radius of the circle), which implies\r\n" );
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document.write( "    a =  =  centimeters.\r\n" );
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document.write( "Next, the area of an equilateral triangle with the side \"a\" is  .\r\n" );
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document.write( "Therefore, the area of our triangle is   =  cm^2 = 129.9038 cm^2,  approximately.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see the Sine law theorem in this formulation, look into the lesson\r
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\n" ); document.write( "\n" ); document.write( " - Law of sines - the Geometric Proof \r
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\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
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