document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203325>Question 1203325</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There is an antenna on the top of a building. From a location 400 feet from the base of the building, the angle of elevation to the top of the building is measured to be 41°. From the same location, the angle of elevation to the top of the antenna is measured to be 44°. Find the height of the antenna. (Round your answer to three decimal places.)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838786 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=838786\">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 size=4>38.561 feet</font> (approximate)\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "Let's start off with a rough sketch of the diagram<BR>\n" );
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document.write( "The key points are<BR>\n" );
document.write( "A = bottom of the person's feet<BR>\n" );
document.write( "B = location of the person's eye<BR>\n" );
document.write( "C = base of the building<BR>\n" );
document.write( "D = point directly across from B and directly above point C<BR>\n" );
document.write( "E = top of the building<BR>\n" );
document.write( "F = top of the antenna\r<BR>\n" );
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document.write( "We have these variables<BR>\n" );
document.write( "x = distance from E to F = height of the antenna<BR>\n" );
document.write( "y = distance from C to D\r<BR>\n" );
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document.write( "I've marked angle DBE = 41 in green, and angle DBF = 44 in blue.\r<BR>\n" );
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document.write( "Focus on triangle DEB.<BR>\n" );
document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(angle DBE) = DE/BD<BR>\n" );
document.write( "tan(41) = y/400<BR>\n" );
document.write( "y = 400*tan(41)<BR>\n" );
document.write( "This will be used in a <font color=blue>substitution</font> step in the next section.\r<BR>\n" );
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document.write( "Now focus on triangle DBF<BR>\n" );
document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(angle DBF) = FD/BD<BR>\n" );
document.write( "tan(44) = (FE+ED)/BD<BR>\n" );
document.write( "tan(44) = (x+y)/400<BR>\n" );
document.write( "tan(44) = (x+<font color=blue>400*tan(41)</font>)/400 ....... <font color=blue>substitution</font><BR>\n" );
document.write( "400*tan(44) = x+400*tan(41)<BR>\n" );
document.write( "x = 400*tan(44)-400*tan(41)<BR>\n" );
document.write( "x = 400*( tan(44)-tan(41) )<BR>\n" );
document.write( "x = 38.560814796339<BR>\n" );
document.write( "x = <font color=red>38.561</font><BR>\n" );
document.write( "This value is approximate.\r<BR>\n" );
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document.write( "Make sure your calculator is in degree mode.<BR>\n" );
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