document.write( "Question 593657: Find the angle (in degrees) between the two lines:
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Algebra.Com's Answer #376396 by Edwin McCravy(20064)\"\" \"About 
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6x - y + 8 = 0
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document.write( "The correct answer is 84.2° not 83.2°.\r\n" );
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document.write( "The other tutor used a different method from the usual method but he \r\n" );
document.write( "also made an error in finding the angle of the second line. He erroneously\r\n" );
document.write( "used the calculator negative result of tan-1(\"-3%2F11\") = -15.2551187,\r\n" );
document.write( "which is the wrong angle.  That is the 4th quadrant principle value of the\r\n" );
document.write( "inverse tangent, not the 2nd quadrant angle which the second line makes with\r\n" );
document.write( "the x-axis.\r\n" );
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document.write( "He should have gotten the reference angle by finding tan-1(\"3%2F11\") = 15.255118. \r\n" );
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document.write( "Then he should have subtracted that from 180° to get the correct 2nd\r\n" );
document.write( "quadrant angle, 164.7448813°\r\n" );
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document.write( "Then when he subtracted the angles he would have gotten \r\n" );
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document.write( "164.7448813° - 80.53767779° =  84.20729351°\r\n" );
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document.write( "Here is the normal method for finding the angle between two\r\n" );
document.write( "lines given their equations:\r\n" );
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document.write( "The formula for the tangent of the angle between two lines is:\r\n" );
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document.write( "tan(Ɵ) = \"abs%28+%28m%5B1%5D-m%5B2%5D%29%2F%281%2Bm%5B1%5Dm%5B2%5D%29+%29\"\r\n" );
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document.write( "Find the slopes of the two lines, as the other tutor did.\r\n" );
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document.write( "6x - y + 8 = 0\r\n" );
document.write( "        -y = -6x - 8\r\n" );
document.write( "         y = 6x + 8\r\n" );
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document.write( "Compare to\r\n" );
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document.write( "         y = mx + b\r\n" );
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document.write( "Slope = m = 6\r\n" );
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document.write( "We will call that m1\r\n" );
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document.write( "-3x - 11y + 10 = 0\r\n" );
document.write( "          -11y = 3x - 10\r\n" );
document.write( "             y = \"-3%2F11\"x + \"10%2F11\"\r\n" );
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document.write( "Compare to\r\n" );
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document.write( "         y = mx + b\r\n" );
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document.write( "Slope = m = \"-3%2F11\"\r\n" );
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document.write( "We will call that m2\r\n" );
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document.write( "tan(Ɵ) = \"abs%28+%28m%5B1%5D-m%5B2%5D%29%2F%281%2Bm%5B1%5Dm%5B2%5D%29+%29\" = \"abs%28+%286-%28-3%2F11%29%29%2F%281%2B%286%29%28-3%2F11%29%29+%29\" = \"abs%28+%286%2B3%2F11%29%2F%281-18%2F11%29+%29\" = -9.857142867\r\n" );
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document.write( "Ɵ = 84.2072935°\r\n" );
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document.write( "Edwin
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