document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=884120>Question 884120</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The angle of elevation of the top of cell tower B from the top of cell tower A is 30 degrees. The angle of depression of the foot of the cell tower B from the top of cell tower A is 60 degrees. The height of cell tower B is 100 meters. The foot of cell tower A and the foot of cell tower B is in the same horizontal plane.<BR>\n" );
document.write( "What is the height of cell tower A?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #534017 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=534017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the following picture shows the relationship between all the parts.\r<BR>\n" );
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document.write( "see below the picture for the analysis.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/jun2501.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "tan(30) = a/x\r<BR>\n" );
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document.write( "tan(60) = b/x\r<BR>\n" );
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document.write( "solve both these equations for x to get:\r<BR>\n" );
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document.write( "x = a/tan(30)\r<BR>\n" );
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document.write( "x = b/tan(60)\r<BR>\n" );
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document.write( "for ease of presentation, let T30 = tan(30) and T60 = tan(60).\r<BR>\n" );
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document.write( "because they both equal x, then they are both equal to each other so  you get:\r<BR>\n" );
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document.write( "a/T30 = b/T60\r<BR>\n" );
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document.write( "multiply both sides of this equation by T30 to get:\r<BR>\n" );
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document.write( "a = T30/T60 * b\r<BR>\n" );
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document.write( "since a + b = 100, you can solve for b to get b = 100 - a.\r<BR>\n" );
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document.write( "substitute for b in the equation of a = T30/T60 * b to get:\r<BR>\n" );
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document.write( "a = T30/T60 * (100 - a)\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "a = (T30/T60 * 100) - (T30/T60 * a)\r<BR>\n" );
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document.write( "add (T30/T60 * a) to both sides of this equation to get:\r<BR>\n" );
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document.write( "a + (T30/T60 * a) = (T30/T60 * 100)\r<BR>\n" );
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document.write( "factor out the a on the left side of the equation to get:\r<BR>\n" );
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document.write( "a * (1 + T30/T60) = (T30/T60 * 100)\r<BR>\n" );
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document.write( "divide both sides of this equation by (1 + T30/T60) to get:\r<BR>\n" );
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document.write( "a = (T30/T60 * 100) / (1 + T30/T60)\r<BR>\n" );
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document.write( "since T30/T670 = 1/3, you can replace T30/T60 with 1/3 and solve for a to get:\r<BR>\n" );
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document.write( "a = (1/3 * 100) / (1 + 1/3) which becomes:\r<BR>\n" );
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document.write( "a = (1/3 * 100) / (4/3) which becomes:\r<BR>\n" );
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document.write( "a = (1/3) * (3/4) * 100 which becomes:\r<BR>\n" );
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document.write( "a = 25\r<BR>\n" );
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document.write( "since a + b = 100, this means that b = 75 which means that the height of tower A is equal to 75.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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