document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=725262>Question 725262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A motorist noticed that as he got 10 km closer to a mountain, the angle of elevation of the top of the mountain changed from 10 degrees to 70 degrees. 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 #444129 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=444129\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A motorist noticed that as he got 10 km closer to a mountain, the angle of elevation of the top of the mountain changed from 10 degrees to 70 degrees. <BR>\n" );
document.write( "Approximate the height of the mountain.<BR>\n" );
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document.write( "Draw this out, consider the triangle formed the by 10 km and the slant ranges from the two given points. <BR>\n" );
document.write( "The interior angles: 10, 180-70=110, and 60 degrees<BR>\n" );
document.write( "Find the slant range(s) to the top of the mountain from initial position using the law of sines.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%2Fsin%28110%29 ALIGN=MIDDLE  ALT=\"s%2Fsin%28110%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Fsin%2860%29 ALIGN=MIDDLE  ALT=\"10%2Fsin%2860%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cross multiply<BR>\n" );
document.write( ".866s = .9397*10<BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9.397%2F.866 ALIGN=MIDDLE  ALT=\"9.397%2F.866\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = 10.85 km to the top of the mountain<BR>\n" );
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document.write( "A right triangle where the side opposite is the height(h) of the mountain<BR>\n" );
document.write( "sin(10) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2F10.85 ALIGN=MIDDLE  ALT=\"h%2F10.85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = 10.85 * .17365<BR>\n" );
document.write( "h = .32125 km or 321.25 meters high </SPAN>\n" );
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