document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=42272>Question 42272</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An observer measures the angle of evevation to the  top  of a  mountain and  obtains  a value  of  39 degrees. After  moving  100m farther away  from the  mountain,the angle  of elevation is  massured as 38.2 degrees. How  tall is  the mountain? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27420 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27420\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-25%2C375%2C-25%2C375%2C%0D%0Aline%280%2C0%2C350%2C0%29%2C%0D%0Aline%28350%2C0%2C350%2C300%29%2C%0D%0Aline%280%2C0%2C350%2C300%29%2C%0D%0Aline%28250%2C0%2C350%2C300%29%2C%0D%0Alocate%280%2C0%2CA%29%2C%0D%0Alocate%28350%2C0%2CB%29%2C%0D%0Alocate%28350%2C300%2CC%29%2C%0D%0Alocate%28250%2C0%2CD%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let the points C and B denote the top and the base of the mountain respectively.<BR>\n" );
document.write( "When the person was at D, the angle of elevation was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=39%5Eo ALIGN=MIDDLE  ALT=\"39%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and when he moved to A, 100 m away from the mountain, the angle of elevation became <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38.2%5Eo ALIGN=MIDDLE  ALT=\"38.2%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So, in the figure, AD = 100 m; < BAC = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38.2%5Eo ALIGN=MIDDLE  ALT=\"38.2%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >; < BDC = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=39%5Eo ALIGN=MIDDLE  ALT=\"39%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In right-angled triangle ABC,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%2FAB+=+tan%2838.2%5Eo%29 ALIGN=MIDDLE  ALT=\"BC%2FAB+=+tan%2838.2%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB+=+BC%2F%28tan%2838.2%5Eo%29%29 ALIGN=MIDDLE  ALT=\"AB+=+BC%2F%28tan%2838.2%5Eo%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > _____(1)\r<BR>\n" );
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document.write( "In right-angled triangle DBC,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%2FDB+=+tan%2839%5Eo%29 ALIGN=MIDDLE  ALT=\"BC%2FDB+=+tan%2839%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DB+=+BC%2F%28tan%2839%5Eo%29%29 ALIGN=MIDDLE  ALT=\"DB+=+BC%2F%28tan%2839%5Eo%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > _____(2)\r<BR>\n" );
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document.write( "Subtracting (2) from (1) we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB+-+DB+=+BC%2Ftan%2838.2%5Eo%29+-+BC%2Ftan%2839%5Eo%29 ALIGN=MIDDLE  ALT=\"AB+-+DB+=+BC%2Ftan%2838.2%5Eo%29+-+BC%2Ftan%2839%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD+=+BC%28cot%2838.2%5Eo%29+-+cot%2839%5Eo%29%29 ALIGN=MIDDLE  ALT=\"AD+=+BC%28cot%2838.2%5Eo%29+-+cot%2839%5Eo%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC+=+AD%2F%28cot%2838.2%5Eo%29+-+cot%2839%5Eo%29%29 ALIGN=MIDDLE  ALT=\"BC+=+AD%2F%28cot%2838.2%5Eo%29+-+cot%2839%5Eo%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC+=+100%2F%281.270773+-+1.234897%29 ALIGN=MIDDLE  ALT=\"BC+=+100%2F%281.270773+-+1.234897%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or BC = 2787.4 m (approx) = 2.7874 km\r<BR>\n" );
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document.write( "Hence, the reqd. height of the mountain is 2.7874 km. </SPAN>\n" );
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