document.write( "Question 1184962: In triangle ABC, side AB measures |3x -6| side BC measures |x2-2x| and side
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Algebra.Com's Answer #815679 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I think you were given that ABC is a right triangle, perhaps with the right\r\n" );
document.write( "angle at B.  Otherwise, there could be infinitely many solutions.  I'm going\r\n" );
document.write( "to assume that's what you were given.\r\n" );
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document.write( "If ABC is a right triangle, we can use the Pythagorean theorem, \r\n" );
document.write( "assuming AC is the hypotenuse\r\n" );
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document.write( "\"AB%5E2%2BBC%5E2=AC%5E2\"\r\n" );
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document.write( "\"%283x-6%29%5E2%2B%28x%5E2-2x%29%5E2=%282x%2B2%29%5E2\"\r\n" );
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document.write( "That becomes a 4th degree equation with\r\n" );
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document.write( "\"x%5E4+-+4x%5E3+%2B+9x%5E2+-+44x+%2B+32+=+0\"\r\n" );
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document.write( "which has real solutions x=4, and by calculator, \r\n" );
document.write( "real irrational solution x≈0.8262208691\r\n" );
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document.write( "So using x=4,\r\n" );
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document.write( "\"AB=abs%283x-6%29=abs%283%284%29-6%29=abs%2812-6%29=abs%286%29=6\"\r\n" );
document.write( "\"BC=abs%28x%5E2-2x%29=abs%28%284%29%5E2-2%284%29%29=abs%2816-8%29=abs%288%29=8\"\r\n" );
document.write( "\"AC=abs%282x%2B2%29=abs%282%284%29%2B2%29=abs%288%2B2%29=abs%2810%29=10\"\r\n" );
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i)sine of angle A
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document.write( "\"sin%28A%29=BC%2FAC=6%2F10=3%2F5\"\r\n" );
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ii)cosine of angle B
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document.write( "\"cos%28B%29=cos%2890%5Eo%29=0\"\r\n" );
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iii)tangent of angle A
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document.write( "\"tan%28A%29=BC%2FAB=6%2F8=3%2F4\"\r\n" );
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document.write( "That's one solution.\r\n" );
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document.write( "Using the irrational solution x≈0.8262208691\r\n" );
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document.write( "\"AB=abs%283x-6%29=abs%283%280.8262208691%29-6%29=abs%28-3.521337393%29=3.521337393\"\r\n" );
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document.write( "\"AC=abs%282x%2B2%29=abs%282%280.8262208691%29%2B2%29=abs%283.652441738%29=3.652441738\"\r\n" );
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i)sine of angle A
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document.write( "\"sin%28A%29=BC%2FAC=0.9698008137%2F3.652441738=0.2655212275\"\r\n" );
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ii)cosine of angle B
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document.write( "\"cos%28B%29=cos%2890%5Eo%29=0\"\r\n" );
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iii)tangent of angle A
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document.write( "\"tan%28A%29=BC%2FAB=0.9698008137%2F3.521337393=0.2754069564\"\r\n" );
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document.write( "That's another solution.\r\n" );
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document.write( "We could also do it assuming AB is the hypotenuse.\r\n" );
document.write( "We could also do it assuming BC is the hypotenuse.\r\n" );
document.write( "and,\r\n" );
document.write( "We could also do it assuming ABC is not a right triangle, \r\n" );
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document.write( "In the future be sure to copy the problem accurately.\r\n" );
document.write( "copy it very carefully, then check for typos and omissions.\r\n" );
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document.write( "Edwin
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