document.write( "Question 935239: The measure of the angles of a triangle are in the ratio of 4:5:6. Find the measure of the largest angle. \n" ); document.write( "
Algebra.Com's Answer #568413 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let's find ALL the angles instead of just the largest one.\r\n" );
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document.write( "(BTW, the largest angle is the angle opposite the largest side)\r\n" );
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document.write( "Consider the sides to have the lengths 4,5, and 6.  \r\n" );
document.write( "a=4, b=5, c=6\r\n" );
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document.write( "The law of cosines\r\n" );
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document.write( "\"cos%28%22ANGLE%22%29\"\"%22%22=%22%22\"       )\r\n" );
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document.write( "To find angle A:\r\n" );
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document.write( "\"cos%28A%29=%28b%5E2%2Bc%5E2-a%5E2%29%2F%282bc%29\"\r\n" );
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document.write( "\"cos%28A%29=%285%5E2%2B6%5E2-4%5E2%29%2F%282%2A5%2A6%29\"\r\n" );
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document.write( "\"cos%28A%29=%2825%2B36-16%29%2F60\"\r\n" );
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document.write( "\"cos%28A%29=45%2F60\"\r\n" );
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document.write( "\"cos%28A%29=3%2F4\"\r\n" );
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document.write( "Use the calculator\r\n" );
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document.write( "\"A=41.40962211%B0\"\r\n" );
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document.write( "Now we can either switch over to the law of sines or \r\n" );
document.write( "continue with the law of cosines, which I think I'll\r\n" );
document.write( "do:\r\n" );
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document.write( "\"cos%28B%29=%28a%5E2%2Bc%5E2-b%5E2%29%2F%282ac%29\"\r\n" );
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document.write( "\"cos%28B%29=%284%5E2%2B6%5E2-5%5E2%29%2F%282%2A4%2A6%29\"\r\n" );
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document.write( "\"cos%28B%29=%2816%2B36-25%29%2F48\"\r\n" );
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document.write( "\"cos%28B%29=27%2F48\"\r\n" );
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document.write( "\"cos%28A%29=9%2F16\"\r\n" );
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document.write( "Use the calculator\r\n" );
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document.write( "\"A=55.77113367%B0\"\r\n" );
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document.write( "Now we can just add angles A and B and subtract from\r\n" );
document.write( "180° to find angle C.  But as a check we can also \r\n" );
document.write( "find it with the law of cosines then add them to see\r\n" );
document.write( "if they have sum 180°.\r\n" );
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document.write( "\"cos%28C%29=%28a%5E2%2Bb%5E2-c%5E2%29%2F%282ab%29\"\r\n" );
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document.write( "\"cos%28C%29=%284%5E2%2B5%5E2-6%5E2%29%2F%282%2A4%2A5%29\"\r\n" );
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document.write( "\"cos%28C%29=%2816%2B25-36%29%2F40\"\r\n" );
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document.write( "\"cos%28C%29=5%2F40\"\r\n" );
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document.write( "\"cos%28C%29=1%2F8\"\r\n" );
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document.write( "Use the calculator\r\n" );
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document.write( "\"C=82.81924422%B0\"\r\n" );
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document.write( "Now we add them to see if we get 180°:\r\n" );
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document.write( "A=41.40962211°\r\n" );
document.write( "B=55.77113367°\r\n" );
document.write( "C=82.81924422°\r\n" );
document.write( "--------------\r\n" );
document.write( " 180.00000000°\r\n" );
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document.write( "Edwin
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