document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142029>Question 1142029</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Provide a sketch for this information.<BR>\n" );
document.write( "A measuring instrument is used at point P and Q on the same horizontal level to measure the angle of elevation of the top T of a hill. Given that P is 5200m above sea level. PQ = 4000m and the angle of elevation of p and Q are 15degrees and 35degrees respectively, calculate the height of the mountain </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762686 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=762686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your diagram looks like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/060903.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "P and Q are both 5200 meters above sea level.\r<BR>\n" );
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document.write( "triangles PMQ and PMB are formed.\r<BR>\n" );
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document.write( "angle MPQ is 15 degrees.\r<BR>\n" );
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document.write( "angle MQB is 35 degrees.\r<BR>\n" );
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document.write( "the height of MB is equal to x.\r<BR>\n" );
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document.write( "the length of QB is equal to y.\r<BR>\n" );
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document.write( "tan(15) = x / (4000 + y)\r<BR>\n" );
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document.write( "tan(35) = x / y\r<BR>\n" );
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document.write( "solve for x in both equations to get:\r<BR>\n" );
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document.write( "x = (4000 + y) * tan(15)\r<BR>\n" );
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document.write( "x = y * tan(35)\r<BR>\n" );
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document.write( "replace x in the first equation with y * tan(35) to get:\r<BR>\n" );
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document.write( "y * tan(35) = (4000 + y) * tan(15)\r<BR>\n" );
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document.write( "simplify to get y * tan(35) = 4000 * tan(15) + y * tan(15)\r<BR>\n" );
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document.write( "subtract y * tan(15) from both sides of the equation to get:\r<BR>\n" );
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document.write( "y * tan(35) - y * tan(15) = 4000 * tan(15)\r<BR>\n" );
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document.write( "factor out the y to get y * (tan(35) - tan(15)) = 4000 * tan(15)\r<BR>\n" );
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document.write( "divide both sides of the equation by tan(35) - tan(15) to get:\r<BR>\n" );
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document.write( "y = 4000 * tan(15) / (tan(35) - tan(15))\r<BR>\n" );
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document.write( "solve for y to get y = 2479.528227 meters.\r<BR>\n" );
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document.write( "in triangle QMX, solve for x to get x = 2479.528227 * tan(35) = 1736.184356 meters.\r<BR>\n" );
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document.write( "the height of the mountain is x + 5200 = 6936.184356 meters. </SPAN>\n" );
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