document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154847>Question 1154847</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Observers P and Q are located on the side of a hill inclined at 32°to the horizontal. The observer at P determines the angle of elevation to a hot-air balloon to be 52°. At the same time, the observer at Q measures the angle of elevation to the balloon to be 61°. If P is 60m down the hill from Q, find the distance from Q to the balloon. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #777571 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=777571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Observers P and Q are located on the side of a hill inclined at 32°to the horizontal.<BR>\n" );
document.write( " The observer at P determines the angle of elevation to a hot-air balloon to be 52°.<BR>\n" );
document.write( " At the same time, the observer at Q measures the angle of elevation to the balloon to be 61°.<BR>\n" );
document.write( " If P is 60m down the hill from Q, find the distance from Q to the balloon.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Since they just want the dist from Q to the balloon, the fact that it is on a hill can be ignored. (assume the angles are measured from the surface they are on, not to the horizontal). <BR>\n" );
document.write( "Solve a triangle that is formed by P, Q, and B (balloon)<BR>\n" );
document.write( "P = 52 degrees, <BR>\n" );
document.write( "the interior angle at Q: 180 - 61 = 119 degrees <BR>\n" );
document.write( "Angle B = 180 - 52 - 119 = 9 degrees<BR>\n" );
document.write( "Using the law of sines, (p = the dist from Q to B)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Fsin%2852%29 ALIGN=MIDDLE  ALT=\"p%2Fsin%2852%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Fsin%289%29 ALIGN=MIDDLE  ALT=\"60%2Fsin%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cross multiply<BR>\n" );
document.write( "sin(9)*p = 60 * sin(52)<BR>\n" );
document.write( ".1564p = 47.2806<BR>\n" );
document.write( "p = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=47.2806%2F.1564 ALIGN=MIDDLE  ALT=\"47.2806%2F.1564\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "p = 302.3 meters from Q to the balloon </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );