document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189682>Question 1189682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ship sees a lighthouse which is found to be 9.8 km distant through the use of radar. The lighthouse is 3km from a second lighthouse. The angle between the line of sight between the two lighthouses is 30°. What is the angle between the line of sight between the ship and lighthouse 2, when looking from lighthouse 1? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821111 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=821111\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
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document.write( "A = ship's location<BR>\n" );
document.write( "B = lighthouse 1<BR>\n" );
document.write( "C = lighthouse 2\r<BR>\n" );
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document.write( "Angle A = 30 degrees<BR>\n" );
document.write( "Angle B = x degrees<BR>\n" );
document.write( "Angle C = 180-A-B = 180-30-x = 150-x degrees\r<BR>\n" );
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document.write( "Apply the law of sines to find x<BR>\n" );
document.write( "sin(A)/a = sin(C)/c <BR>\n" );
document.write( "sin(30)/3 = sin(150-x)/9.8 <BR>\n" );
document.write( "0.5/3 = sin(150-x)/9.8 <BR>\n" );
document.write( "0.5*9.8 = 3sin(150-x) <BR>\n" );
document.write( "4.9 = 3sin(150-x) <BR>\n" );
document.write( "3*sin(150-x) = 4.9<BR>\n" );
document.write( "sin(150-x) = 1.633333 approximately\r<BR>\n" );
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document.write( "We run into a problem. Recall that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%3C=+sin%28x%29+%3C=+1 ALIGN=MIDDLE  ALT=\"-1+%3C=+sin%28x%29+%3C=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, i.e. the outputs of sine are restricted to the interval between -1 and 1. <BR>\n" );
document.write( "So it's impossible to have sin(150-x) be 1.63 as that's larger than 1.\r<BR>\n" );
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document.write( "No triangle is possible with those specified side lengths and angle. <BR>\n" );
document.write( "Please contact your teacher for clarification.<BR>\n" );
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