document.write( "Question 919189: ABCD is a parallelogram. AB=8 BC=10 and diagonal AC=13. determine the measure of angle BAD to the nearest minute \n" ); document.write( "
Algebra.Com's Answer #557594 by Edwin McCravy(20063)\"\" \"About 
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document.write( "We use the Law of cosines to find ∠ABC\r\n" );
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document.write( "Chosse AC as the \"THIRD SIDE\"\r\n" );
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document.write( "AC² = AB² + BC² - 2·AB·BC·cos(∠ABC)\r\n" );
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document.write( "13² = 8² + 10² - 2·8·10·cos(∠ABC)\r\n" );
document.write( "169 = 64 + 100 - 160·cos(∠ABC)\r\n" );
document.write( "169 = 164 - 160·cos(∠ABC)\r\n" );
document.write( "5 = -160·cos(∠ABC)\r\n" );
document.write( "\"-5%2F160\" = cos(∠ABC)\r\n" );
document.write( "-0.03125 = cos(∠ABC)\r\n" );
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document.write( "So ∠ABC is an obtuse angle in the \r\n" );
document.write( "second quadrant. so we find the reference angle\r\n" );
document.write( "by finding the inverse cosine of +0.03125 which is\r\n" );
document.write( "88.20921534° and subtract from 180° and get \r\n" );
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document.write( "∠ABC = 91.79078466°\r\n" );
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document.write( "Since two adjacent angles of a parallelogram are \r\n" );
document.write( "supplementary, we can find ∠BAD by subtracting ∠ABC \r\n" );
document.write( "from 180°.\r\n" );
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document.write( "But we'll just get 88.20921534° again which is the same as\r\n" );
document.write( "the reference angle for ∠ABC.\r\n" );
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document.write( "Therefore ∠BAD = 88.20921534°\r\n" );
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document.write( "To get that to the nearest minute we multiply the\r\n" );
document.write( "decimal part 0.20921534 by 60 getting 12.55229204\r\n" );
document.write( "which rounds to 13 minutes.\r\n" );
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document.write( "Answer: ∠BAD = 88°13'\r\n" );
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document.write( "Edwin
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