document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197746>Question 1197746</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation<BR>\n" );
document.write( "(to the peak) is 3.5 o . After you drive 13 miles closer to the mountain, the angle of elevation is 9 o .<BR>\n" );
document.write( "Approximate the height of 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 #831142 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=831142\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "This is one way to draw the diagram.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/M82KxO0.png\"><BR>\n" );
document.write( "A = 1st observation point<BR>\n" );
document.write( "B = 2nd observation point<BR>\n" );
document.write( "C = base of the mountain<BR>\n" );
document.write( "D = peak of the mountain\r<BR>\n" );
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document.write( "The goal is to determine the length of segment CD, aka the height of the mountain, which I'll call h.<BR>\n" );
document.write( "Another variable we'll use is x which is the distance from B to C.\r<BR>\n" );
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document.write( "Focus your attention on triangle BCD.<BR>\n" );
document.write( "Use the tangent ratio to say this<BR>\n" );
document.write( "tan(angle) = opp/adj<BR>\n" );
document.write( "tan(B) = CD/BC<BR>\n" );
document.write( "tan(9) = h/x<BR>\n" );
document.write( "x*tan(9) = h<BR>\n" );
document.write( "x = h/tan(9)<BR>\n" );
document.write( "x = (1/tan(9))*h<BR>\n" );
document.write( "x = 6.3137515h<BR>\n" );
document.write( "This is approximate.<BR>\n" );
document.write( "Your calculator needs to be in degree mode.\r<BR>\n" );
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document.write( "Now move your focus to triangle ACD.<BR>\n" );
document.write( "tan(angle) = opp/adj<BR>\n" );
document.write( "tan(A) = CD/AC<BR>\n" );
document.write( "tan(3.5) = h/(x+13)<BR>\n" );
document.write( "tan(3.5) = h/(6.3137515h+13)<BR>\n" );
document.write( "0.0611626 = h/(6.3137515h+13)\r<BR>\n" );
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document.write( "Let's solve for h.<BR>\n" );
document.write( "0.0611626 = h/(6.3137515h+13)<BR>\n" );
document.write( "0.0611626(6.3137515h+13) = h<BR>\n" );
document.write( "0.0611626*6.3137515h+0.0611626*13 = h<BR>\n" );
document.write( "0.3861655h+0.7951138 = h<BR>\n" );
document.write( "0.7951138 = h-0.3861655h<BR>\n" );
document.write( "0.7951138 = 0.6138345h<BR>\n" );
document.write( "0.6138345h = 0.7951138<BR>\n" );
document.write( "h = 0.7951138/0.6138345<BR>\n" );
document.write( "h = 1.29532276208<BR>\n" );
document.write( "h = 1.2953\r<BR>\n" );
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document.write( "Answer: <font color=red>Approximately 1.2953 miles tall</font>\r<BR>\n" );
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document.write( "Extra info:<BR>\n" );
document.write( "Multiply this with 5280 to convert to feet<BR>\n" );
document.write( "1.2953 miles = 5280*1.2953 = 6839.184 feet<BR>\n" );
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