document.write( "Question 1205897: Sides of a triangle are 8,11,13.find the largest angle of the triangle
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Algebra.Com's Answer #842984 by Theo(13342)\"\" \"About 
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the largest angle will be opposite the largest side.
\n" ); document.write( "if the triangle is ABC, then side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C.\r
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\n" ); document.write( "\n" ); document.write( "you can use the law of cosines to find angle C.
\n" ); document.write( "the law of cosines is c^2 = a^2 + b^2 - 2abcos(C).\r
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\n" ); document.write( "\n" ); document.write( "that becomes 13^2 = 8^2 + 11^2 - 2*8*11*cos(C).
\n" ); document.write( "add 2*8*11*cos(C) to both sides of the and subtract 13^2 from both sides of the equation to get 2*8*11*cos(C) = 8^2 + 11^2 - 13^2.
\n" ); document.write( "divide both sides of the equation by (2*8*11) to get cos(C) = (8^2 + 11^2 - 13^2) / (2 * 8 * 11) = .0909091909.
\n" ); document.write( "arcos(.0909090909) = 84.78409143 degrees
\n" ); document.write( "that's angle C.\r
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\n" ); document.write( "\n" ); document.write( "you can use the law of sines to find angle B.
\n" ); document.write( "that law says sin(C) / c = sin(B) / b.
\n" ); document.write( "that becomes sin(84.78409143)/13 = sin(B)/11.
\n" ); document.write( "solve for sin(B) to get sin(B) = sin(84.78409143)/13 * 11 = .8426500885.
\n" ); document.write( "arcsin(.842650885) = 57.42102961 degrees.\r
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\n" ); document.write( "\n" ); document.write( "since the sum of the interior angles of a triangle = 180 degrees, then angle A = 180 - 84.78409143 - 57.42102961 = 37.79487896.\r
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\n" ); document.write( "\n" ); document.write( "the largest angle is opposite the largest side and the smallest angle is opposite the smallest side with the middle angle opposite the middle side.\r
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\n" ); document.write( "\n" ); document.write( "here are the results in a table of values.
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document.write( "side       sine of angle      angle\r\n" );
document.write( "8          .612836428         37.79487896\r\n" );
document.write( "11         .8426500885        57.42102961\r\n" );
document.write( "13         .9958591955        84.78409143\r\n" );
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\n" ); document.write( "sum of the angles is 180 as it should be.
\n" ); document.write( "here's my diagram
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