document.write( "Question 935883: Find the equation of the line passing through (4,7) and has an angle of 60 degrees with the line x=4. \n" ); document.write( "
Algebra.Com's Answer #569258 by Edwin McCravy(20062)\"\" \"About 
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document.write( "There are TWO solutions to this problem, for there are two ways a\r\n" );
document.write( "line can have an angle of 60 degrees with the line x=4.\r\n" );
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document.write( "Here is one solution:\r\n" );
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document.write( "We are to find the equation of the black line:\r\n" );
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document.write( "We need the slope of the black line.  The slope is \"RISE%2FRUN\"\r\n" );
document.write( "We have the RISE which is BC or 7.  We need the RUN.\r\n" );
document.write( "Since the triangle ABC is a 30-60-90 right triangle, \r\n" );
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document.write( "AC = 2(BC) = 2(7) = 14\r\n" );
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document.write( "ABē+BCē = ACē\r\n" );
document.write( " ABē+7ē = 14ē\r\n" );
document.write( " ABē+49 = 196\r\n" );
document.write( "    ABē = 147\r\n" );
document.write( "     AB = √147\r\n" );
document.write( "     AB = √49*3\r\n" );
document.write( "     AB = 7√3\r\n" );
document.write( "Now we have the RUN.\r\n" );
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document.write( "So the slope is \"RISE%2FRUN=BC%2FAB=7%2F%287sqrt%283%29%29=1%2Fsqrt%283%29=sqrt%283%29%2F3\"\r\n" );
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document.write( "The black line goes through (4,7), so we use the point-slope form:\r\n" );
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document.write( "y - y1 = m(x - x1)\r\n" );
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document.write( "where (x1,y1) = (4,-7) and m = \"sqrt%283%29%2F3\"\r\n" );
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document.write( "y - (-7) = sqrt(3)/3}}}(x - 4)\r\n" );
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document.write( "   y + 7 = sqrt(3)/3}}}x - 4sqrt(3)/3}}}\r\n" );
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document.write( "       y = sqrt(3)/3}}}x - 4sqrt(3)/3}}} - 7\r\n" );
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document.write( "That's one solution.  The other solution is done this way:\r\n" );
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document.write( "The slope of that black line will be the negative of the slope of the\r\n" );
document.write( "black line in the first solution.  That is m = \"-sqrt%283%29%2F3\"  I'll \r\n" );
document.write( "let you do this second solution.\r\n" );
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document.write( "Edwin
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