document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=289726>Question 289726</A>: <I><SPAN STYLE=\"word-break: break-all;\"> While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is 2.5 degrees. After you drive 17 miles closer to the mountain, the angle of elevation is 9 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 #209973 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=209973\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> While traveling across flat land, you notice a mountain directly in front of you.<BR>\n" );
document.write( " The angle of elevation to the peak is 2.5 degrees.<BR>\n" );
document.write( " After you drive 17 miles closer to the mountain, the angle of elevation is 9 degrees.<BR>\n" );
document.write( " Approximate the height of the mountain.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "represent this with a scalene triangle, where<BR>\n" );
document.write( "A = 2.5 degrees<BR>\n" );
document.write( "B = (180-9) = 171 degrees<BR>\n" );
document.write( "C = 180 - 171 - 2.5 = 6.5 degrees<BR>\n" );
document.write( "c = 17<BR>\n" );
document.write( "Find side b using the law of sines: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Fsin%28c%29 ALIGN=MIDDLE  ALT=\"c%2Fsin%28c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fsin%28b%29 ALIGN=MIDDLE  ALT=\"b%2Fsin%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2Fsin%286.5%29 ALIGN=MIDDLE  ALT=\"17%2Fsin%286.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fsin%28171%29 ALIGN=MIDDLE  ALT=\"b%2Fsin%28171%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Sin(6.5)b = 17*sin(171)<BR>\n" );
document.write( ":<BR>\n" );
document.write( ".1132b = 2.659<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.659%2F.1132 ALIGN=MIDDLE  ALT=\"2.659%2F.1132\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = 23.49 mi (from angle A to the top of the mountains)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Side b is the hypotenuse of a right triangle at the base of the mountain<BR>\n" );
document.write( "formed by the mountain top and a line to point A<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use the sine of 2.5,<BR>\n" );
document.write( "height (h) of the mountain will be the side opposite<BR>\n" );
document.write( "Sin(2.5) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2F23.49 ALIGN=MIDDLE  ALT=\"h%2F23.49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".0436 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2F23.49 ALIGN=MIDDLE  ALT=\"h%2F23.49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = .0436 * 23.49<BR>\n" );
document.write( "h = 1.02462 mi is the mountain height<BR>\n" );
document.write( "0r<BR>\n" );
document.write( "1.02462 * 5280 = 5410 ft high<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );