document.write( "Question 1092330: Given that A and B are acute angles such that sin A = 3/5 and cos B = 5/13, calculate the value of sin(A+B) \n" ); document.write( "
Algebra.Com's Answer #706937 by ikleyn(52803)\"\" \"About 
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document.write( "1.  Since sin(A) = \"3%2F5\",  cos(A) = \"sqrt%281+-+sin%5E2%28A%29%29\" = \"sqrt%281-%283%2F5%29%5E2%29\" = \"sqrt%281-9%2F25%29\" = \"sqrt%2825-9%29%2F25%29\" = \"sqrt%2816%2F25%29\" = \"4%2F5%29\".\r\n" );
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document.write( "2.  Since cos(B) = \"5%2F13\",  sin(B) = \"sqrt%281+-+cos%5E2%28B%29%29\" = \"sqrt%281-%285%2F13%29%5E2%29\" = \"sqrt%281-25%2F169%29\" = \"sqrt%28169-25%29%2F169%29\" = \"sqrt%28144%2F169%29\" = \"12%2F13%29\".\r\n" );
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document.write( "3.  Now sin(A+B) = sin(A)*cos(B) + cos(A)*sin(B) = \"%283%2F5%29%2A%285%2F13%29+%2B+%284%2F5%29%2A%2812%2F13%29\" = \"15%2F65+%2B+48%2F65\" = \"63%2F65\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer.  sin(A+B) = \"63%2F65\".\r
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