Algebra.Com's Answer #811986 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "In ∆ACS, AC = 12, SA = 8 and SC = 16. Determine the measures of all the interior angles of the triangle.
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document.write( "Use the cosine law\r\n" );
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document.write( " c^2 = a^2 + b^2 - 2bccos(C),\r\n" );
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document.write( "where \"a\", \"b\", \"c\" are the lengths of the three sides of a triangle, and C is the angle opposite to the side \"c\".\r\n" );
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document.write( "It gives\r\n" );
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document.write( " cos(C) =  .\r\n" );
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document.write( "Apply this formula to each angle of the triangle\r\n" );
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document.write( " angle A, a= 12, b= 8, c= 16; cos(A) =  = -0.25;\r\n" );
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document.write( " A = arccos(0.25) = 1.823 radians = 104.48 degrees.\r\n" );
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document.write( " angle C, a= 12, b= 16, c= 8; cos(A) =  = 0.875;\r\n" );
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document.write( " C = arccos(0.875) = 0.505 radians = 28.96 degrees.\r\n" );
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document.write( " angle S, a= 8, b= 16, c= 12; cos(S) =  = 0.6875;\r\n" );
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document.write( " C = arccos(68.75) = 0.813 radians = 46.57 degrees.\r\n" );
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document.write( "The problem is just solved: all the angles are found.\r\n" );
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document.write( "As a conclusion, I will check the sum of angles 104.48 + 28.96 + 46.57 = 180 degrees, ! correct !\r\n" );
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document.write( "Solved.\r
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