document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1076426>Question 1076426</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There is a small island in the middle of a 100m wide river and a tall tree <BR>\n" );
document.write( "stands on the island. P and Q are points directly opposite each other on the two<BR>\n" );
document.write( " banks, and in the line with the tree. If the angles of elevation of the top of <BR>\n" );
document.write( "tree from P and Q are 30 and 45 , find the distance of p from the tree. \r<BR>\n" );
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document.write( "I would be grateful if you help me to solve this problem. <BR>\n" );
document.write( "Thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #691295 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=691295\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let T equal the top of the tree and B equal the bottom of the tree.\r<BR>\n" );
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document.write( "you have 2 triangles formed with a common side being side TB\r<BR>\n" );
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document.write( "the first triangle formed is PTB with angle P equal to 30 degrees.\r<BR>\n" );
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document.write( "the second triangle formed is QTB with angle Q eaual to 45 degrees.\r<BR>\n" );
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document.write( "both triangle PTB and QTB are part of the overall triangle formed of PTQ.\r<BR>\n" );
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document.write( "TB is assumed to be perpendicular to PQ.\r<BR>\n" );
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document.write( "therefore triangles PTB and QTB are assumed to be right triangles.\r<BR>\n" );
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document.write( "you are given that the length of PQ is equal to 100 meters.\r<BR>\n" );
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document.write( "tan(30) = TB / PB\r<BR>\n" );
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document.write( "tan(45) = TB / BQ\r<BR>\n" );
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document.write( "solve for TB in both these formulas to get:\r<BR>\n" );
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document.write( "TB = PB * tan(30)\r<BR>\n" );
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document.write( "TB = BQ * tan(45)\r<BR>\n" );
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document.write( "since they are both equal to TB, then you get:\r<BR>\n" );
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document.write( "PB * tan(30) = BQ * tan(45)\r<BR>\n" );
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document.write( "let x equal the length of PB.\r<BR>\n" );
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document.write( "therefore 100 - x equals the length of BQ.\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "x * tan(30) = (100 - x) * tan(45)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "x * tan(30) = 100 * tan(45) - tan(45) * x\r<BR>\n" );
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document.write( "add tan(45) * x to both sides of this equation to get:\r<BR>\n" );
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document.write( "x * tan(30) + x * tan(45) = 100 * tan(45)\r<BR>\n" );
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document.write( "factor out the x to get:\r<BR>\n" );
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document.write( "x * (tan(30) + tan(45)) = 100 * tan(45)\r<BR>\n" );
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document.write( "divide both sides of the equation by (tan(30) + tan(45)) to get:\r<BR>\n" );
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document.write( "x = (100 * tan(45) / (tan(30) + tan(45))\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 63.39745962\r<BR>\n" );
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document.write( "that's the length of PB.\r<BR>\n" );
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document.write( "100 - x = 36.60254038\r<BR>\n" );
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document.write( "that's the length of BQ\r<BR>\n" );
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document.write( "you were asked to find the distance of p from the tree.\r<BR>\n" );
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document.write( "that would be the length of PB.\r<BR>\n" );
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document.write( "TB is the height of the tree and that turns out to be 36.60254038 meters.\r<BR>\n" );
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document.write( "your diagram would look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/041502.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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