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 #844960 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=844960\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 400 feet from the base of the mountain and the angle is 25 degrees.<BR>\n" );
document.write( "another 500 feet = 900 feet from the base of the mountain and the angle is 20 degrees.\r<BR>\n" );
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document.write( "let x be the height of the mountain.\r<BR>\n" );
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document.write( "tan(25) = x/409<BR>\n" );
document.write( "tan(20) = x/900.\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 = tan(25) * 400 = 186.5230633.<BR>\n" );
document.write( "x = tan(20) * 900 = 327.5732108.\r<BR>\n" );
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document.write( "there's a problem.\r<BR>\n" );
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document.write( "the value of x should have been the same in both equations.<BR>\n" );
document.write( "it is not.\r<BR>\n" );
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document.write( "assuming the original measurements were correct, there's a problem with either the other angle or the additional feet from the base of the mountain.\r<BR>\n" );
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document.write( "if we assume the additional angle is correct, then:<BR>\n" );
document.write( "tan(20) = 186.5230633 / y<BR>\n" );
document.write( "y is the total feet from the mountain when the angle of elevation is 20 degrees.<BR>\n" );
document.write( "solve for y to get y = 186.5230633 / tan(20) = 512.4679045.<BR>\n" );
document.write( "the additional distance from the base of the mountain is that minus the original distance = 512.4679045 minus 400 = 112.4679045 feet.\r<BR>\n" );
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document.write( "if we assume the additional distance is correct, then:<BR>\n" );
document.write( "tan(b) = x / y = 186.5230633 / 900 = .2072478481.<BR>\n" );
document.write( "b is the other angle we are looking for that is farther from the base of the mountain.<BR>\n" );
document.write( "angle b = arctan (.2072478481) = 11.7086694 degrees.\r<BR>\n" );
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document.write( "here's my diagram of the situation as i understand it.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/050604.jpg\">\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo\r<BR>\n" );
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