document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203323>Question 1203323</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 200-foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is 14°, and that the angle of depression to the bottom of the tower is 2°. How far is the person from the monument? (Round your answer to three decimal places.)  </SPAN>\n" );
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document.write( "Answer: <font color=red size=4>703.609 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 = base of the building<BR>\n" );
document.write( "B = location of the person's eye<BR>\n" );
document.write( "C = base of the monument<BR>\n" );
document.write( "D = location on monument at the same height level as the person's eye<BR>\n" );
document.write( "E = top of the monument\r<BR>\n" );
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document.write( "We have these variables<BR>\n" );
document.write( "x = distance from B to D = distance from A to C<BR>\n" );
document.write( "y = distance from C to D\r<BR>\n" );
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document.write( "Note how segment DE is 200-y feet long so that CE = CD+DE = y + (200-y) = 200\r<BR>\n" );
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document.write( "Let's focus on triangle BCD.<BR>\n" );
document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(angle DBC) = CD/BD<BR>\n" );
document.write( "tan(2) = y/x<BR>\n" );
document.write( "y = x*tan(2)<BR>\n" );
document.write( "This will be used later in a <font color=blue>substitution</font> step.\r<BR>\n" );
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document.write( "Now 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(14) = (200-y)/x<BR>\n" );
document.write( "tan(14) = (200-<font color=blue>x*tan(2)</font>)/x ........ <font color=blue>substitution</font><BR>\n" );
document.write( "x*tan(14) = 200-x*tan(2)<BR>\n" );
document.write( "x*tan(14)+x*tan(2) = 200<BR>\n" );
document.write( "x*( tan(14)+tan(2) ) = 200<BR>\n" );
document.write( "x = 200/( tan(14)+tan(2) )<BR>\n" );
document.write( "x = 703.609019511759 approximately<BR>\n" );
document.write( "x = <font color=red>703.609</font>\r<BR>\n" );
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document.write( "Make sure your calculator is in degree mode.<BR>\n" );
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