document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=925918>Question 925918</A>: <I><SPAN STYLE=\"word-break: break-all;\"> an airplane took off from the airport and started flying toward its destination 210 miles due east. After flying 80 miles east, it encountered a storm and altered its course by turning left 22'. when it was past the storm , it turned right 30'and flew in a straight line until it reached its destination. how far was  the plane from its destination when it made the 30' turn ?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #561911 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=561911\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is a sketch that illustrates the situation. (The angles and proportions are not right on purpose).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C200%2C-15%2C35%2C-5%2C15%2C%0D%0Agreen%28line%2810%2C10%2C15%2C15%29%29%2C%0D%0Ared%28circle%28-12%2C0%2C0.5%29%29%2C%0D%0Ared%28circle%2832%2C0%2C0.5%29%29%2Clocate%2818.5%2C6%2Cx%29%2C%0D%0Aline%28-12%2C0%2C32%2C0%29%2Cline%280%2C0%2C10%2C10%29%2Cline%2810%2C10%2C32%2C0%29%2C%0D%0Alocate%28-15%2C-1%2Cstart%29%2Clocate%2826%2C-1%2Cdestination%29%2C%0D%0Ared%28arc%280%2C0%2C10%2C10%2C-45%2C0%29%29%2Cred%28arc%2810%2C10%2C10%2C10%2C-45%2C24.4%29%29%2C%0D%0Alocate%281.5%2C2.5%2Cred%2822%5Eo%29%29%2Clocate%2811%2C12%2Cred%2830%5Eo%29%29%2C%0D%0Alocate%28-7%2C1.5%2C80%29%2Clocate%2815%2C1.5%2C130%29%2Clocate%289%2C-3%2C210%29%2C%0D%0Aarrow%288.5%2C-3.5%2C-12%2C-3.5%29%2Carrow%2811.5%2C-3.5%2C32%2C-3.5%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The plane was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210-80=130 ALIGN=MIDDLE  ALT=\"210-80=130\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles from its destination when it made the first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2822%5Eo%29 ALIGN=MIDDLE  ALT=\"%2822%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > turn.<BR>\n" );
document.write( "It was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles from its destination when it made the second <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2830%5Eo%29 ALIGN=MIDDLE  ALT=\"%2830%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > turn.<BR>\n" );
document.write( "We can use law of sines on the triangle you can see in the sketch.<BR>\n" );
document.write( "The angle at the top of that triangle is the supplementary angle to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%5Eo ALIGN=MIDDLE  ALT=\"30%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > angle of the second turn.<BR>\n" );
document.write( "It measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo-30%5Eo=150%5Eo ALIGN=MIDDLE  ALT=\"180%5Eo-30%5Eo=150%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and like all supplementary angles, has the same sine:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28150%5Eo%29=sin%2830%5Eo%29=0.5 ALIGN=MIDDLE  ALT=\"sin%28150%5Eo%29=sin%2830%5Eo%29=0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (an exact <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5=1%2F2 ALIGN=MIDDLE  ALT=\"0.5=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > number).<BR>\n" );
document.write( "Law of sines says that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=130%2Fsin%28150%5Eo%29=x%2Fsin%2822%5Eo%29 ALIGN=MIDDLE  ALT=\"130%2Fsin%28150%5Eo%29=x%2Fsin%2822%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2822%5Eo%29=0.3746 ALIGN=MIDDLE  ALT=\"sin%2822%5Eo%29=0.3746\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded) to get a very accurate answer.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=130%2Fsin%28150%5Eo%29=x%2Fsin%2822%5Eo%29 ALIGN=MIDDLE  ALT=\"130%2Fsin%28150%5Eo%29=x%2Fsin%2822%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=130%2F0.5=x%2F0.3746 ALIGN=MIDDLE  ALT=\"130%2F0.5=x%2F0.3746\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=130%2A0.3746%2F0.5=x ALIGN=MIDDLE  ALT=\"130%2A0.3746%2F0.5=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=97.4%29 ALIGN=MIDDLE  ALT=\"highlight%28x=97.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded).<BR>\n" );
document.write( "The plane was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2897.4%29 ALIGN=MIDDLE  ALT=\"highlight%2897.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles from its destination when it made the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%5Eo ALIGN=MIDDLE  ALT=\"30%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > turn. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );