Algebra.Com's Answer #818904 by ikleyn(52803)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "An observer 9 meters horizontally away from the tower observes its angle of elevation to be only one half
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document.write( "as much as the angle of elevation of the same tower when he moves 5 meters nearer towards the tower.
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document.write( "How high is the tower?
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document.write( " It is a good Trigonometry problem, and it deserves a detailed explanation.\r
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document.write( " See my solution below. Read it attentively.\r
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document.write( "Let h be the height of the tower.\r\n" );
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document.write( "First position is 9 meters from the tower. In this position,\r\n" );
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document.write( " tan(a) =  , where \"a\" is the angle of elevation in this position. (1)\r\n" );
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document.write( "Next position is (9-5) = 4 meters from the tower. In this position,\r\n" );
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document.write( " tan(b) =  , where \"b\" is the angle of elevation in this position. (2)\r\n" );
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document.write( "We are given b = 2a. Hence,\r\n" );
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document.write( " tan(b) = tan(2a) = (use the basic Trigonometry formula) =  = \r\n" );
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document.write( " =  = (simplify) =  =  =  .\r\n" );
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document.write( "Thus from (2) we have THIS EQUATION\r\n" );
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document.write( " = .\r\n" );
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document.write( "Cancel common factor \"h\" in both sides; then cross-multiply to get\r\n" );
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document.write( " 18*4 = 81 - h^2\r\n" );
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document.write( " 72 = 81 - h^2\r\n" );
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document.write( " h^2 = 81 - 72 = 9.\r\n" );
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document.write( "Hence, h =  = 3.\r\n" );
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document.write( "ANSWER. The tower height is 3 meters.\r\n" );
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document.write( "Solved and thoroughly explained.\r
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