document.write( "Question 205114: The following facts are true about triangle ABC:\r
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Algebra.Com's Answer #154841 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
Edwin's solution. Stanbon is wrong to say angle A could be 150°. It can only be 30°. Here's why:\r
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document.write( "By the law of sines:\r\n" );
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document.write( "\"BC%2Fsin%28A%29=AC%2Fsin%28B%29\"\r\n" );
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document.write( "\"x%2Fsin%28A%29=%28x%2Asqrt%283%29%29%2Fsin%28%22120%B0%22%29\" \r\n" );
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document.write( "Cross-multiply:\r\n" );
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document.write( "\"x%2Asqrt%283%29sin%28A%29=x%2Asin%28%22120%B0%22%29\"\r\n" );
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document.write( "Divide both sides by \"x%2Asqrt%283%29\"\r\n" );
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document.write( "\"sin%28A%29=sin%28%22120%B0%22%29%2Fsqrt%283%29\"\r\n" );
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document.write( "We know that \"sin%28%22120%B0%22%29=sqrt%283%29%2F2\", so substituting:\r\n" );
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document.write( "\"sin%28A%29=%28sqrt%283%29%2F2%29%2Fsqrt%283%29\"\r\n" );
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document.write( "Write as a division:\r\n" );
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document.write( "\"sin%28A%29=%28sqrt%283%29%2F2%29\"\"%22%F7%22sqrt%283%29\"\r\n" );
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document.write( "Invert and multiply\r\n" );
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document.write( "\"sin%28A%29=%28sqrt%283%29%2F2%29\"\"%22%2A%22%281%2Fsqrt%283%29%29\"\r\n" );
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document.write( "\"sin%28A%29=%28cross%28sqrt%283%29%29%2F2%29\"\"%22%2A%22%281%2Fcross%28sqrt%283%29%29%29\"\r\n" );
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document.write( "\"sin%28A%29=1%2F2\"\r\n" );
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document.write( "There are two angles between 0° and 180° which\r\n" );
document.write( "have sine \"1%2F2\", they are 30° and 150°, but\r\n" );
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document.write( "angle A cannot be 150°, because angle B is 120°,\r\n" );
document.write( "and that would make two angles in the same\r\n" );
document.write( "triangle with sum more than 180° which is \r\n" );
document.write( "impossible.  So angle A can only be 30°.\r\n" );
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document.write( "Edwin
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