document.write( "Question 1148362: In the diagram to the bottom, circle with center O has a radius of 8cm. Segment AT is tangent to the circle. Angle AOT=60 degrees, and AX=XY (this length is labeled m). Find the length of m. \r
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Algebra.Com's Answer #769736 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " There is EXTREMELY SIMPLE solution.\r
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document.write( "From the diagram,  we have an isosceles triangle AXO with equal sides lengths  | AX | = | OX |.\r\n" );
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document.write( "The base AO of this triangle is 16 units long, since it is the hypotenuse of the (30° - 60° - 90°) triangle AOT.\r\n" );
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document.write( "The angle A is 30°.\r\n" );
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document.write( "Draw the altitude  XZ  in the triangle AXO.\r\n" );
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document.write( "Then you will get right angled triangle AXZ with the long leg  AZ of the length of 8 = 16/2 units and the angle A of 30°.\r\n" );
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document.write( "Thus  cos(A) = cos(30°) =  = ,\r\n" );
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document.write( "which implies  m =  =  = 9.237 units approximately, if you want to have the numerical value.\r\n" );
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document.write( "ANSWER.  m =  = 9.237 (approximately).\r\n" );
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