document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207217>Question 1207217</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person standing 400 ft from the base of a mountain measures the angle of elevation from the ground to the top of the mountain to be 25° The person then walks 500 ft straight back and measures the angle of elevation to now be 20°. How tall is the mountain?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844963 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=844963\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red>829.227965 feet</font> (approximate)\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "Review this similar question<BR>\n" );
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document.write( "On that solution page I provide the derivation of this formula<BR>\n" );
document.write( "h = d*u*v/(u-v)<BR>\n" );
document.write( "where,<BR>\n" );
document.write( "h = height of the object<BR>\n" );
document.write( "d = distance between observation points<BR>\n" );
document.write( "u = tangent of larger angle<BR>\n" );
document.write( "v = tangent of smaller angle\r<BR>\n" );
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document.write( "In this case,<BR>\n" );
document.write( "d = 500<BR>\n" );
document.write( "u = tan(25)<BR>\n" );
document.write( "v = tan(20)\r<BR>\n" );
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document.write( "So we can quickly determine the mountain height to be:<BR>\n" );
document.write( "h = d*u*v/(u-v)<BR>\n" );
document.write( "h = 500*tan(25)*tan(20)/( tan(25) - tan(20) )<BR>\n" );
document.write( "h = <font color=red>829.227965 feet approximately</font><BR>\n" );
document.write( "Make sure your calculator is in degrees mode.\r<BR>\n" );
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document.write( "Tutor Theo incorrectly shows the 400 ft spanning from the original observation point to a point directly under the mountain peak; whereas it should be from the initial observation point to the base of the mountain. Luckily this value is not needed so we can ignore it.<BR>\n" );
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