document.write( "Question 1082130: From a point outside the equilateral triangle, the distances of the 10, 10, and 18. Find the dimension of the triangle. \n" ); document.write( "

Algebra.Com's Answer #696310 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "From a point outside the equilateral triangle, the distances $\"highlight%28to_the_triangle_vertices%29\"$ are 10, 10, and 18 units. Find the dimension of the triangle.
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document.write( "0.  Make a sketch to follow my arguments.\r\n" );
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document.write( "    Let the triangle will be ABC, and the point outside be D.\r\n" );
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document.write( "    Connect D by segments with A, B and C. \r\n" );
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document.write( "    Let CD = 10, BD = 10 and AD = 18.\r\n" );
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document.write( "    Let the length of the side of the triangle ABC be x.\r\n" );
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document.write( "1.  The quadrilateral ACBD is a kite, since AB = AC  and  BD = CD.\r\n" );
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document.write( "    Therefore, AD is the angle bisector to angles A and D.\r\n" );
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document.write( "    It implies that the angle DAB is 30 degs.\r\n" );
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document.write( "2.  Now consider the triangle ABD\r\n" );
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document.write( "    Its side AD is 18 units long, side BD is 10 units long and side AB is x.\r\n" );
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document.write( "    The angle DAB is 30 degs.\r\n" );
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document.write( "    Apply the Cosines law theorem:\r\n" );
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document.write( "     = ,   or\r\n" );
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document.write( "     = 0.\r\n" );
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document.write( "    It is your quadratic equation to find x.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The setup is done. The rest is just arithmetic.\r
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\n" ); document.write( "\n" ); document.write( "I got the answer x = $\"%2818%2Asqrt%283%29-2%2Asqrt%2819%29%29%2F2\"$ .\r
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