document.write( "Question 1207589: In the diagram, ABCD is a square. Find sin angle PAQ.\r
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Algebra.Com's Answer #845550 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Maybe you want exact values, not decimal approximations.\r\n" );
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document.write( "Use the properties of a square and the Pythagorean theorem\r\n" );
document.write( "on the 3 right triangles to get all the measures in red.\r\n" );
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document.write( "Then use the law of cosines to find the cos(PAQ):\r\n" );
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document.write( "\"PQ%5E2\"\"%22%22=%22%22\"\"AP%5E2%2BAQ%5E2-2%2AAP%2AAQ%2Acos%28PAQ%29\"\r\n" );
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document.write( "\"sqrt%2813%29%5E2\"\"%22%22=%22%22\"\"sqrt%2829%29%5E2%2Bsqrt%2834%29%5E2-2%2Asqrt%2829%29%2Asqrt%2834%29%2Acos%28PAQ%29\"\r\n" );
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document.write( "\"13\"\"%22%22=%22%22\"\"29%2B34-2%2Asqrt%2834%29%2Asqrt%2829%29%2Acos%28PAQ%29\"\r\n" );
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document.write( "\"13\"\"%22%22=%22%22\"\"63-2%2Asqrt%28986%29cos%28PAQ%29\"\r\n" );
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document.write( "\"2%2Asqrt%28986%29%2Acos%28PAQ%29\"\"%22%22=%22%22\"\"63-13\"\r\n" );
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document.write( "\"2%2Asqrt%28986%29%2Acos%28PAQ%29\"\"%22%22=%22%22\"\"50\"\r\n" );
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document.write( "\"cos%28PAQ%29\"\"%22%22=%22%22\"\"50%2F%282%2Asqrt%28986%29%29\"\r\n" );
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document.write( "\"cos%28PAQ%29\"\"%22%22=%22%22\"\"25%2Fsqrt%28986%29\"\r\n" );
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document.write( "Then use the identity\r\n" );
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document.write( "\"sin%5E2%28PAQ%29\"\"%22%22=%22%22\"\"1-cos%5E2%28PAQ%29\"\r\n" );
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document.write( "\"sin%5E2%28PAQ%29\"\"%22%22=%22%22\"\"1-%2825%2Fsqrt%28986%29%29%5E2\"\r\n" );
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document.write( "\"sin%5E2%28PAQ%29\"\"%22%22=%22%22\"\"1-625%2F986\"\r\n" );
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document.write( "\"sin%5E2%28PAQ%29\"\"%22%22=%22%22\"\"361%2F986\"\r\n" );
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document.write( "\"sin%28PAQ%29\"\"%22%22=%22%22\"\"sqrt%28361%2F986%29\"\r\n" );
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document.write( "\"sin%28PAQ%29\"\"%22%22=%22%22\"\"sqrt%28expr%28361%2F986%29%2Aexpr%28986%2F986%29%29\"\r\n" );
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document.write( "\"sin%28PAQ%29\"\"%22%22=%22%22\"\"sqrt%28361%2A986%29%2F986%29%29\"\r\n" );
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document.write( "\"sin%28PAQ%29\"\"%22%22=%22%22\"\"%2819%2Asqrt%28986%29%29%2F986%29%29\"\r\n" );
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document.write( "That is approximately 0.6050832675, which agrees with the other tutor.\r\n" );
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document.write( "Edwin
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