document.write( "Question 827006: The question can be viewed here:
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Algebra.Com's Answer #498431 by AnlytcPhil(1810)\"\" \"About 
You can put this solution on YOUR website!
Question 827006
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document.write( "AP, PQ and QR are three equal line segments inclined at angles\r\n" );
document.write( "\"alpha\",\"2alpha\", and\"3alpha\" respectively to line\r\n" );
document.write( "segment AB.  Show that\r\n" );
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document.write( "tan(< BAR) = \"RB%2FAB\" = \r\n" );
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document.write( "Draw PS and QT perpendicular to AB, PU and QV parallel to AB.\r\n" );
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document.write( "\"PS%2FAP=sin%28alpha%29\"\r\n" );
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document.write( "\"PS=AP%2Asin%28alpha%29\"\r\n" );
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document.write( "< QPU = \"2alpha\"  Parallel lines cut by transversal\r\n" );
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document.write( "\"QU%2FPQ=sin%28QPU%29=sin%282alpha%29\"\r\n" );
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document.write( "\"QU=PQ%2Asin%282alpha%29\"\r\n" );
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document.write( "\"QT=QU%2BUT=QU%2BPS=PQ%2Asin%282alpha%29%2BAP%2Asin%28alpha%29\"\r\n" );
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document.write( "\"RV%2FQR=sin%283alpha%29\"\r\n" );
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document.write( "\"RV=QR%2Asin%283alpha%29\"\r\n" );
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document.write( "\"RB+=+RV%2BVB+=+RV%2BQT+=+QR%2Asin%283alpha%29%2BPQ%2Asin%282alpha%29%2BAP%2Asin%28alpha%29\"\r\n" );
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document.write( "Since we are given AP=PQ=QR\r\n" );
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document.write( "\"RB=AP%2Asin%28alpha%29%2BAP%2Asin%282alpha%29%2BAP%2Asin%283alpha%29\"\r\n" );
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document.write( "\"RB=AP%28sin%28alpha%29%2Bsin%282alpha%29%2Bsin%283alpha%29%29\"\r\n" );
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document.write( "Exactly similar to above using cosines instead of sines and\r\n" );
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document.write( "AS, PU and QV instead of PSQU and RV, you can prove\r\n" );
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document.write( "\"RB=AP%28sin%28alpha%29%2Bsin%282alpha%29%2Bsin%283alpha%29%29\"\r\n" );
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document.write( "then \r\n" );
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document.write( "Cancel the AP's and get\r\n" );
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document.write( "tan(BAR) = \r\n" );
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document.write( "  Edwin
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