document.write( "Question 816390: Will you please help me solve:
\n" ); document.write( "0\n" ); document.write( "If cosx= 8/17 and tany= 5/12, find sin(x+y) \n" ); document.write( "

Algebra.Com's Answer #491537 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "since the cosine is the adjacent over the hypotenuse, \r\n" );
document.write( "and we are given that the cosine of x is 8 over 17, we \r\n" );
document.write( "will draw a right triangle with an adjacent side of 8\r\n" );
document.write( "and a hypotenuse of 17.  Then the angle in that \r\n" );
document.write( "triangle that has 8 for its adjacent side will be \r\n" );
document.write( "angle x.\r\n" );
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document.write( "Since the tangent is the opposite over the adjacent, \r\n" );
document.write( "and we are given that the tangent of y is 5 over 12, \r\n" );
document.write( "we will draw a right triangle with an opposite side \r\n" );
document.write( "of 5 and an adjacent side of 12.  Then the angle in \r\n" );
document.write( "that triangle that has 5 for its opposite side and \r\n" );
document.write( "12 for its adjacent side will be angle y.\r\n" );
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document.write( " \r\n" );
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document.write( "Now we will find the missing side in each of those\r\n" );
document.write( "triangles using the Pythagorean theorem:\r\n" );
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document.write( " c² = a² + b²         c² = a² + b²\r\n" );
document.write( "17² = 8² + b²         c² = 12² + 5²\r\n" );
document.write( "289 = 64 + b²         c² = 144 + 25\r\n" );
document.write( "225 = b²              c² = 169\r\n" );
document.write( " 15 = b                c = 13\r\n" );
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document.write( "Now we use the identity\r\n" );
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document.write( "sin(x+y) = sin(x)cos(y) + cos(x)sin(y)\r\n" );
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document.write( "and use the sides of those triangles to substitute\r\n" );
document.write( "the trig ratios:\r\n" );
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document.write( "sin(x+y) =  =  =  \r\n" );
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document.write( "Edwin

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