document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=42529>Question 42529</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine if the following triangles have no solutions, one solution, or two solutions:\r<BR>\n" );
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document.write( "1.  A=130 degrees, a=19, b=11.<BR>\n" );
document.write( "2.  A=45 degrees, a=4&#8730;2, b=8.<BR>\n" );
document.write( "3.  A=32 degrees, a=16, b=21.<BR>\n" );
document.write( "4.  A=90 degrees, a=25, b=15.\r<BR>\n" );
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document.write( "Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27818 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27818\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am showing the procedure to solve this type of problems. I am solving the first question. Do the rest yourself. That will nake you understand this things better.<BR>\n" );
document.write( "For the first problem, A=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=130%5Eo ALIGN=MIDDLE  ALT=\"130%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a=19, b=11.\r<BR>\n" );
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document.write( "The sine rule states:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fsin%28A%29+=+b%2Fsin%28B%29 ALIGN=MIDDLE  ALT=\"a%2Fsin%28A%29+=+b%2Fsin%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2Fsin%28130%5Eo%29+=+11%2Fsin%28B%29 ALIGN=MIDDLE  ALT=\"19%2Fsin%28130%5Eo%29+=+11%2Fsin%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2Asin%28B%29+=+11%2Asin%28130%5Eo%29 ALIGN=MIDDLE  ALT=\"19%2Asin%28B%29+=+11%2Asin%28130%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28B%29+=+%2811%2Asin%28130%5Eo%29%29%2F19 ALIGN=MIDDLE  ALT=\"sin%28B%29+=+%2811%2Asin%28130%5Eo%29%29%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28B%29+=+%2811%2A0.766%29%2F19 ALIGN=MIDDLE  ALT=\"sin%28B%29+=+%2811%2A0.766%29%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28B%29+=+0.4435 ALIGN=MIDDLE  ALT=\"sin%28B%29+=+0.4435\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+sin%5E-1%280.4435%29 ALIGN=MIDDLE  ALT=\"B+=+sin%5E-1%280.4435%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+26.33%5Eo ALIGN=MIDDLE  ALT=\"B+=+26.33%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+180%5Eo+-+A+-+B ALIGN=MIDDLE  ALT=\"C+=+180%5Eo+-+A+-+B\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+180%5Eo+-+135%5Eo+-+26.33%5Eo+=+18.67%5Eo ALIGN=MIDDLE  ALT=\"C+=+180%5Eo+-+135%5Eo+-+26.33%5Eo+=+18.67%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, apply sine rule again<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fsin%28A%29+=+c%2Fsin%28C%29 ALIGN=MIDDLE  ALT=\"a%2Fsin%28A%29+=+c%2Fsin%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2Fsin%28135%5Eo%29+=+c%2Fsin%2818.67%5Eo%29 ALIGN=MIDDLE  ALT=\"19%2Fsin%28135%5Eo%29+=+c%2Fsin%2818.67%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+%2819%2Asin%2818.67%5Eo%29%29%2Fsin%28135%5Eo%29 ALIGN=MIDDLE  ALT=\"c+=+%2819%2Asin%2818.67%5Eo%29%29%2Fsin%28135%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+%2819%2A0.32%29%2F0.766 ALIGN=MIDDLE  ALT=\"c+=+%2819%2A0.32%29%2F0.766\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+7.94 ALIGN=MIDDLE  ALT=\"c+=+7.94\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, we observe a > b + c [since 19 > 11 + 7.94].<BR>\n" );
document.write( "But, for a triangle to exist, the sum of any two sides must be greater than the third.<BR>\n" );
document.write( "So this triangle does not exist.<BR>\n" );
document.write( "So there is no solution.\r<BR>\n" );
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document.write( "Solve the other problems in a similar way.<BR>\n" );
document.write( "If the condition: \"Sum of any two sides of a triangle is greater than the third\" is not violated then the triangle exists and hence the solution is unique i.e. only one solution. Otherwise there is no solution. </SPAN>\n" );
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