document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204365>Question 1204365</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. Solve the triangle, if possible. Round your answers to the nearest tenth. (If not possible, enter IMPOSSIBLE.)<BR>\n" );
document.write( "b = 9, 𝛽 = 98°, 𝛾 = 30° </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840566 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=840566\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "𝛼 = Greek letter alpha (lowercase)<BR>\n" );
document.write( "𝛽 = Greek letter beta (lowercase)<BR>\n" );
document.write( "𝛾 = Greek letter gamma (lowercase)\r<BR>\n" );
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document.write( "𝛼 = unknown for now<BR>\n" );
document.write( "𝛽 = 98°<BR>\n" );
document.write( "𝛾 = 30°\r<BR>\n" );
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document.write( "𝛼 + 𝛽 + 𝛾 = 180<BR>\n" );
document.write( "𝛼 + 98 + 30 = 180<BR>\n" );
document.write( "𝛼 + 128 = 180<BR>\n" );
document.write( "𝛼 = 180-128<BR>\n" );
document.write( "𝛼 = 52\r<BR>\n" );
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document.write( "Sides<BR>\n" );
document.write( "a = unknown<BR>\n" );
document.write( "b = 9<BR>\n" );
document.write( "c = unknown\r<BR>\n" );
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document.write( "Angles<BR>\n" );
document.write( "𝛼 = 52°<BR>\n" );
document.write( "𝛽 = 98°<BR>\n" );
document.write( "𝛾 = 30°\r<BR>\n" );
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document.write( "Law of Sines<BR>\n" );
document.write( "sin(𝛼)/a = sin(𝛽)/b<BR>\n" );
document.write( "sin(52)/a = sin(98)/9<BR>\n" );
document.write( "9*sin(52) = a*sin(98)<BR>\n" );
document.write( "a = 9*sin(52)/sin(98)<BR>\n" );
document.write( "a = 7.16179487789919 approximately<BR>\n" );
document.write( "a = 7.2<BR>\n" );
document.write( "Please make sure your calculator is set to degree mode.\r<BR>\n" );
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document.write( "Also,<BR>\n" );
document.write( "sin(𝛽)/b = sin(𝛾)/c<BR>\n" );
document.write( "sin(98)/9 = sin(30)/c<BR>\n" );
document.write( "c*sin(98) = 9*sin(30)<BR>\n" );
document.write( "c = 9*sin(30)/sin(98)<BR>\n" );
document.write( "c = 4.54422407633379 approximately<BR>\n" );
document.write( "c = 4.5\r<BR>\n" );
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document.write( "The fully solved triangle has these angles and sides:<BR>\n" );
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document.write( "<tr><TD >Angles</TD><TD >Sides</TD></tr><tr><TD >𝛼 = 52°<BR>\n" );
document.write( "𝛽 = 98°<BR>\n" );
document.write( "𝛾 = 30°</TD><TD >a = 7.2 approximately<BR>\n" );
document.write( "b = 9<BR>\n" );
document.write( "c = 4.5 approximately</TD></tr>\n" );
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document.write( "Diagram<BR>\n" );
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document.write( "Only one unique triangle is possible due to the AAS congruence theorem.\r<BR>\n" );
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document.write( "More practice<BR>\n" );
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document.write( "</font> </SPAN>\n" );
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