document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204918>Question 1204918</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When Josephine stood south of the base of Mount Apo, in the Philippines, and looked up to the top, the angle of elevation was 21°. When Josephine drove 4.5 km closer, she found that the angle of elevation increased by 22°. What is the height of Mount Apo? (Note: the actual height of Mount Apo is 2954m) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841458 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=841458\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0A%0D%0Aline%28-3%2C-2%2C2%2C-2%29%2Cline%282%2C-2%2C2%2C2%29%2Cline%282%2C2%2C-1%2C-2%29%2Cline%282%2C2%2C-3%2C-2%29%2C%0D%0A%0D%0Aline%281.6%2C-2%2C1.6%2C-1.6%29%2Cline%281.6%2C-1.6%2C2%2C-1.6%29%2C%0D%0A%0D%0Alocate%28-3.14%2C-2.28%2C%22A%22%29%2Clocate%28-1.2%2C-2.3%2C%22B%22%29%2Clocate%281.96%2C-2.38%2C%22C%22%29%2Clocate%282.2%2C2.36%2C%22D%22%29%2Clocate%28-2.2%2C-1.5%2B0.2%2C21%5Eo%29%2Clocate%28-0.4%2C-1.54%2B0.2%2C43%5Eo%29%2Clocate%28-2.2%2C-2.3%2B0.2%2C%224.5%22%29%2Clocate%280.38%2C-2.36%2B0.2%2C%22x%22%29%2Clocate%282.28%2C0.28%2C%22y%22%29%2C%0D%0A%0D%0Alocate%28-4%2C-4%2Cmatrix%281%2C4%2C%22Diagram%22%2C%22not%22%2C%22to%22%2C%22scale%22%29%29%0D%0A%0D%0A%29%0D%0A%0D%0A%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Josephine starts at point A. Then moves to point B.<BR>\n" );
document.write( "C is the base of the mountain<BR>\n" );
document.write( "D is the peak\r<BR>\n" );
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document.write( "The 43 degree angle is from computing 21+22 = 43.\r<BR>\n" );
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document.write( "Focus on right triangle BCD<BR>\n" );
document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(B) = CD/BC<BR>\n" );
document.write( "tan(43) = y/x<BR>\n" );
document.write( "y = x*tan(43)\r<BR>\n" );
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document.write( "Now focus on right triangle ACD.<BR>\n" );
document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(A) = CD/AC<BR>\n" );
document.write( "tan(A) = CD/(AB+BC)<BR>\n" );
document.write( "tan(21) = y/(4.5+x)<BR>\n" );
document.write( "tan(21) = x*tan(43)/(4.5+x)<BR>\n" );
document.write( "(4.5+x)*tan(21) = x*tan(43)<BR>\n" );
document.write( "4.5*tan(21)+x*tan(21) = x*tan(43)<BR>\n" );
document.write( "4.5*tan(21) = x*tan(43)-x*tan(21)<BR>\n" );
document.write( "x*tan(43)-x*tan(21) = 4.5*tan(21)<BR>\n" );
document.write( "x*(tan(43) - tan(21)) = 4.5*tan(21)<BR>\n" );
document.write( "x = 4.5*tan(21)/(tan(43) - tan(21))<BR>\n" );
document.write( "x = 3.148428 kilometers approximately\r<BR>\n" );
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document.write( "y = x*tan(43)<BR>\n" );
document.write( "y = 3.148428*tan(43)<BR>\n" );
document.write( "y = 2.935957 kilometers approximately\r<BR>\n" );
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document.write( "When rounding to 3 decimal places, we get 2.936 km which converts to 2936 meters. <BR>\n" );
document.write( "Not too far off compared to the actual height 2954 meters.<BR>\n" );
document.write( "The discrepancy could be based on these factors<ul><li>Rounding error</li><li>Josephine might have made a mistake measuring either of the angles or the 4.5 km distance</li></ul>\r<BR>\n" );
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document.write( "The shortcut formula to find the height is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=height+=+d%2Atan%28B%29%2Atan%28A%29%2F%28tan%28B%29-tan%28A%29%29 ALIGN=MIDDLE  ALT=\"height+=+d%2Atan%28B%29%2Atan%28A%29%2F%28tan%28B%29-tan%28A%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = distance between observation points<BR>\n" );
document.write( "A and B = angles of elevation where B > A\r<BR>\n" );
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document.write( "More practice<BR>\n" );
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document.write( "and<BR>\n" );
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document.write( "</font> </SPAN>\n" );
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