document.write( "Question 1068724: The Law of Cosines applies to which cases of oblique triangles?\r
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Algebra.Com's Answer #684008 by Edwin McCravy(20061)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "It's actually both C and D, although I wouldn't be surprised if your\r\n" );
document.write( "teacher or book author says the law of cosines cannot be used for SSA.\r\n" );
document.write( "If they do, they're wrong!\r\n" );
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document.write( "It's not normally used for SSA but it can be used.  Below is\r\n" );
document.write( "proof that the SSA case can be solved completely using the\r\n" );
document.write( "law of cosines only, and not using the law of sines at all.\r\n" );
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document.write( "The law of cosines can be stated any of these three ways:\r\n" );
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document.write( "1.  a² = b² + c² -2bc cos(A)\r\n" );
document.write( "2.  b² = a² + c² -2ac cos(B)\r\n" );
document.write( "3.  c² = a² + b² -2ab cos(C)\r\n" );
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document.write( "Suppose a=8, c=7, C = 60°\r\n" );
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document.write( "Use form 3:\r\n" );
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document.write( "c² = a² + b² -2ab cos(C)\r\n" );
document.write( "7² = 8² + b² - 2(8)(b)cos(60°)\r\n" );
document.write( "49 = 64 + b² - 2(8)(b)(1/2)\r\n" );
document.write( "49 = 64 + b² - 8b\r\n" );
document.write( " 0 = b² - 8b + 15\r\n" );
document.write( " 0 = (b - 5)(b - 3)\r\n" );
document.write( "     b - 5 = 0;  b - 3 = 0\r\n" );
document.write( "         b = 5;      b = 3\r\n" );
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document.write( "Then for b = 5 use the law of cosines form 1\r\n" );
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document.write( "a² = b² + c² -2bc cos(A)\r\n" );
document.write( "8² = 5² + 7² -2(5)(7) cos(A)\r\n" );
document.write( "64 = 25 + 49 - 70cos(A)\r\n" );
document.write( "64 = 74 - 70cos(A)\r\n" );
document.write( "-10 = -70cos(A)\r\n" );
document.write( "1/7 = cos(A)\r\n" );
document.write( "81.8° = A\r\n" );
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document.write( "Then find the third angle by adding \r\n" );
document.write( "angle B by adding A and C and subtracting \r\n" );
document.write( "from 180°\r\n" );
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document.write( "81.8° + 60° = 141.8°\r\n" );
document.write( "180° - 141.8° = 38.2°\r\n" );
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document.write( "So we solved the SSA case completely by\r\n" );
document.write( "the law of cosines, without using the law of \r\n" );
document.write( "sines at all.\r\n" );
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document.write( "This was an ambiguous case and we can solve for\r\n" );
document.write( "the other solution the same way, using b = 5.\r\n" );
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document.write( "So the law of cosines can be used for the SSA case.\r\n" );
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document.write( "Edwin
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