document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204641>Question 1204641</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume 𝛼 is opposite side a, 𝛽 is opposite side b, and 𝛾 is opposite side c. Determine whether there is no triangle, one triangle, or two triangles. Then solve each triangle, if possible. Round each answer to the nearest tenth. (If not possible, enter IMPOSSIBLE. Below, enter your answers so that 𝛼1 is smaller than 𝛼2.)<BR>\n" );
document.write( "a = 7,<BR>\n" );
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document.write( "b = 3,<BR>\n" );
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document.write( "𝛽 = 24° </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841024 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+7 ALIGN=MIDDLE  ALT=\"a+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+3 ALIGN=MIDDLE  ALT=\"b+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta=+24 ALIGN=MIDDLE  ALT=\"beta=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
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document.write( "using Law of Cosine, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=sqrt%28a%5E2%2Bc%5E2-2%2Aa%2Ac%2Acos%28beta%29%29 ALIGN=MIDDLE  ALT=\"b=sqrt%28a%5E2%2Bc%5E2-2%2Aa%2Ac%2Acos%28beta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=sqrt%287%5E2%2Bc%5E2-2%2A7%2Ac%2Acos%2824%29%29 ALIGN=MIDDLE  ALT=\"3=sqrt%287%5E2%2Bc%5E2-2%2A7%2Ac%2Acos%2824%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=49%2Bc%5E2-14%2Ac%2Acos%2824%29 ALIGN=MIDDLE  ALT=\"9=49%2Bc%5E2-14%2Ac%2Acos%2824%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=49%2Bc%5E2-14%2Ac%2A0.9135454576426 ALIGN=MIDDLE  ALT=\"9=49%2Bc%5E2-14%2Ac%2A0.9135454576426\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=49%2Bc%5E2-12.7896c ALIGN=MIDDLE  ALT=\"9=49%2Bc%5E2-12.7896c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=49%2Bc%5E2-12.7896c-9 ALIGN=MIDDLE  ALT=\"0=49%2Bc%5E2-12.7896c-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2-12.7896c%2B40=0 ALIGN=MIDDLE  ALT=\"c%5E2-12.7896c%2B40=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using quadratic formula and got:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5.5 ALIGN=MIDDLE  ALT=\"c=5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=7.3 ALIGN=MIDDLE  ALT=\"c=7.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then angle alpha is\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5.5 ALIGN=MIDDLE  ALT=\"c=5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=cos%5E-1%28%28b%5E2%2Bc%5E2-a%5E2%29%2F%282bc%29%29 ALIGN=MIDDLE  ALT=\"alpha=cos%5E-1%28%28b%5E2%2Bc%5E2-a%5E2%29%2F%282bc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=cos%5E-1%28%283%5E2%2B5.5%5E2-7%5E2%29%2F%282%2A3%2A5.5%29%29 ALIGN=MIDDLE  ALT=\"alpha=cos%5E-1%28%283%5E2%2B5.5%5E2-7%5E2%29%2F%282%2A3%2A5.5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=107 ALIGN=MIDDLE  ALT=\"alpha=107\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( " if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=7.3 ALIGN=MIDDLE  ALT=\"c=7.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=cos%5E-1%28%283%5E2%2B7.3%5E2-7%5E2%29%2F%282%2A3%2A7.3%29%29 ALIGN=MIDDLE  ALT=\"alpha=cos%5E-1%28%283%5E2%2B7.3%5E2-7%5E2%29%2F%282%2A3%2A7.3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=72.3 ALIGN=MIDDLE  ALT=\"alpha=72.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then angle gamma is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=gamma=180-%2824%2B107%29 ALIGN=MIDDLE  ALT=\"gamma=180-%2824%2B107%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=gamma=49 ALIGN=MIDDLE  ALT=\"gamma=49\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
document.write( "\n" );
document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=gamma=180-%2824%2B72.3%29 ALIGN=MIDDLE  ALT=\"gamma=180-%2824%2B72.3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=gamma=83.7 ALIGN=MIDDLE  ALT=\"gamma=83.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "so, there are two triangles:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281%29.+%0D%0A%0D%0A%7B%7B%7Ba+=+7 ALIGN=MIDDLE  ALT=\"highlight%281%29.+%0D%0A%0D%0A%7B%7B%7Ba+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+3 ALIGN=MIDDLE  ALT=\"b+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5.5 ALIGN=MIDDLE  ALT=\"c=5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=107 ALIGN=MIDDLE  ALT=\"alpha=107\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta=+24 ALIGN=MIDDLE  ALT=\"beta=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=gamma=49 ALIGN=MIDDLE  ALT=\"gamma=49\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282%29.+%0D%0A%0D%0A%7B%7B%7Ba+=+7 ALIGN=MIDDLE  ALT=\"highlight%282%29.+%0D%0A%0D%0A%7B%7B%7Ba+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+3 ALIGN=MIDDLE  ALT=\"b+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=7.3 ALIGN=MIDDLE  ALT=\"c=7.3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=72.3 ALIGN=MIDDLE  ALT=\"alpha=72.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta=+24 ALIGN=MIDDLE  ALT=\"beta=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=gamma=83.7 ALIGN=MIDDLE  ALT=\"gamma=83.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );