document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1093693>Question 1093693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve using the Law of Sines and a scaled drawing. If two triangles exist, solve both completely. Round to the nearest tenth.<BR>\n" );
document.write( "side a = 23.9 mi<BR>\n" );
document.write( "&#8736;B = 64°<BR>\n" );
document.write( "side b = 22.0 mi<BR>\n" );
document.write( "Select one:<BR>\n" );
document.write( " a. &#8736;A = 77.5°, &#8736;C = 38.5°, c = 15.2 mi<BR>\n" );
document.write( " b. &#8736;A = 102.5°, &#8736;C = 13.5°, c = 5.7 mi<BR>\n" );
document.write( " c. &#8736;A = 77.5°, &#8736;C = 38.5°, c = 15.2 mi or &#8736;A = 102.5°, &#8736;C = 13.5°, c = 5.7 m<BR>\n" );
document.write( " d. Not possible </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #708324 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=708324\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> law of sines says:\r<BR>\n" );
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document.write( "a / sin(A) = b / sin(B) = c / sin(C)\r<BR>\n" );
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document.write( "you are given:\r<BR>\n" );
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document.write( "B = 64 degrees<BR>\n" );
document.write( "b = 22<BR>\n" );
document.write( "a = 23.9\r<BR>\n" );
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document.write( "a / sin(A) = b / sin(B) becomes 23.9 / sin(A) = 22 / sin(64)\r<BR>\n" );
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document.write( "solve for sin(A) to get sin(A) = 23.9 * sin(64) / 22 = .9764\r<BR>\n" );
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document.write( "solve for A to get A = arcsin(.9764) = 77.5 degrees.\r<BR>\n" );
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document.write( "C is equal to 180 - 77.5 - 64 = 38.5 degrees.\r<BR>\n" );
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document.write( "c / sin(C) = b / sin(B) becomes c / sin(38.5) = 22 / sin(64)\r<BR>\n" );
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document.write( "solve for c to get c = 22 * sin(38.5) / sin(64) = 15.2\r<BR>\n" );
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document.write( "one solution is:\r<BR>\n" );
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document.write( "a. &#8736;A = 77.5°, &#8736;C = 38.5°, c = 15.2 mi\r<BR>\n" );
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document.write( "since the given angle B is not included between the given sides a and b, then there is the possibility of another solution.\r<BR>\n" );
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document.write( "that solution could be in the second quadrant.\r<BR>\n" );
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document.write( "check for a solution in the second quadrant as follows:\r<BR>\n" );
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document.write( "180 - 77.5 = 102.5 in the second quadrant.<BR>\n" );
document.write( "that means that A is possibly 102.5<BR>\n" );
document.write( "if possible, C would be equal to 180 - 102.5 - 64 = 13.5<BR>\n" );
document.write( "that's possible so there is a second possible solution.\r<BR>\n" );
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document.write( "if you tried to do the same thing with 38.5, then you would have found it is not possible.<BR>\n" );
document.write( "180 - 38.5 = 141.5 + 64 = something greater than 180, therefore not possible.\r<BR>\n" );
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document.write( "solve for c as follows:\r<BR>\n" );
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document.write( "c / sin(C) = b / sin(B) which becomes c/sin(13.5) = 22/sin(64).\r<BR>\n" );
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document.write( "solve for c to get c = 22 * sin(13.5) / sin(64) = 5.7\r<BR>\n" );
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document.write( "your second possible solution is:\r<BR>\n" );
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document.write( "b. &#8736;A = 102.5°, &#8736;C = 13.5°, c = 5.7 mi\r<BR>\n" );
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document.write( "since both a. and b. are possible, and they are both included in c., then your solution is:\r<BR>\n" );
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document.write( "c. &#8736;A = 77.5°, &#8736;C = 38.5°, c = 15.2 mi or &#8736;A = 102.5°, &#8736;C = 13.5°, c = 5.7 m\r<BR>\n" );
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document.write( "a reasonably scaled diagram of your solutions is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/091511.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "in this diagram:\r<BR>\n" );
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document.write( "angle A is on top.<BR>\n" );
document.write( "Angle B is lower left.<BR>\n" );
document.write( "Angle C is lower right.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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