document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198061>Question 1198061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To measure the height of a mountain, a surveyor takes two sightings of a peak 900 meters apart on a direct line to the mountain.  The two different angles of elevation are, 47 and 35 degrees. If the transit is 2 meters high, how tall is the mountain?\r<BR>\n" );
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document.write( "One of the following is the answer.  Which one?\r<BR>\n" );
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document.write( "A) 1660 meters<BR>\n" );
document.write( "B) 1752 meters <BR>\n" );
document.write( "C) 1818 meters<BR>\n" );
document.write( "D) 2059 meters <BR>\n" );
document.write( "E) 2278 meters  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831604 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=831604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "This is one way to do the drawing<BR>\n" );
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document.write( "The observation points are at B and C. <BR>\n" );
document.write( "The mountain is represented by segment FD, which has a height of h+2.\r<BR>\n" );
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document.write( "Segments:<BR>\n" );
document.write( "AB = x<BR>\n" );
document.write( "BC = 900<BR>\n" );
document.write( "FA = h<BR>\n" );
document.write( "AD = CE = 2<BR>\n" );
document.write( "FD = h+2\r<BR>\n" );
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document.write( "Angles:<BR>\n" );
document.write( "angle ABF = 47 degrees<BR>\n" );
document.write( "angle ACF = 35 degrees\r<BR>\n" );
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document.write( "Let<BR>\n" );
document.write( "u = tan(47)<BR>\n" );
document.write( "v = tan(35)<BR>\n" );
document.write( "which will help us do the symbolic operations shown below a bit easier.\r<BR>\n" );
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document.write( "Focus on triangle ABF.<BR>\n" );
document.write( "Use the tangent ratio to say<BR>\n" );
document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(B) = FA/AB<BR>\n" );
document.write( "tan(47) = h/x<BR>\n" );
document.write( "u = h/x<BR>\n" );
document.write( "ux = h<BR>\n" );
document.write( "h = ux\r<BR>\n" );
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document.write( "Now focus on triangle ACF<BR>\n" );
document.write( "tan(C) = FA/AC<BR>\n" );
document.write( "tan(35) = h/(x+900)<BR>\n" );
document.write( "v = h/(x+900)<BR>\n" );
document.write( "v(x+900) = h<BR>\n" );
document.write( "vx + 900v = h<BR>\n" );
document.write( "vx + 900v = ux<BR>\n" );
document.write( "900v = ux - vx<BR>\n" );
document.write( "900v = (u-v)x<BR>\n" );
document.write( "x = 900v/(u-v)\r<BR>\n" );
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document.write( "Therefore,<BR>\n" );
document.write( "h = ux<BR>\n" );
document.write( "h = u*900v/(u-v)<BR>\n" );
document.write( "h = 900uv/(u-v)<BR>\n" );
document.write( "we have this fairly tidy formula to calculate the height based on the tangents of the angles mentioned, and also based on the distance between the observation points from B to C.\r<BR>\n" );
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document.write( "Now plug in the definitions for u and v mentioned earlier<BR>\n" );
document.write( "h = 900uv/(u-v)<BR>\n" );
document.write( "h = 900*tan(47)*tan(35)/(tan(47)-tan(35))<BR>\n" );
document.write( "h = 1815.86000966682\r<BR>\n" );
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document.write( "which leads to:<BR>\n" );
document.write( "h+2 = 1815.86000966682+2 = 1817.86000966681\r<BR>\n" );
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document.write( "When rounding to the nearest whole number we get <font color=red>1818 meters</font> as the final answer.\r<BR>\n" );
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document.write( "Related Question<BR>\n" );
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