document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204286>Question 1204286</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( "𝛼 = 36°, 𝛾 = 62°, a = 20 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840437 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=840437\">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 = 36°<BR>\n" );
document.write( "𝛽 = unknown<BR>\n" );
document.write( "𝛾 = 62°\r<BR>\n" );
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document.write( "𝛼 + 𝛽 + 𝛾 = 180 <BR>\n" );
document.write( "36 + 𝛽 + 62 = 180 <BR>\n" );
document.write( "98 + 𝛽 = 180 <BR>\n" );
document.write( "𝛽 = 180 - 98<BR>\n" );
document.write( "𝛽 = 82°\r<BR>\n" );
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document.write( "Sides<BR>\n" );
document.write( "a = 20<BR>\n" );
document.write( "b = unknown<BR>\n" );
document.write( "c = unknown\r<BR>\n" );
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document.write( "Angles<BR>\n" );
document.write( "𝛼 = 36°<BR>\n" );
document.write( "𝛽 = 82°<BR>\n" );
document.write( "𝛾 = 62°\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(36)/20 = sin(82)/b<BR>\n" );
document.write( "b*sin(36) = 20*sin(82)<BR>\n" );
document.write( "b = 20*sin(82)/sin(36)<BR>\n" );
document.write( "b = 33.6948933264092 approximately<BR>\n" );
document.write( "b = 33.7<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(𝛼)/a = sin(𝛾)/c<BR>\n" );
document.write( "sin(36)/20 = sin(62)/c<BR>\n" );
document.write( "c*sin(36) = 20*sin(62)<BR>\n" );
document.write( "c = 20*sin(62)/sin(36)<BR>\n" );
document.write( "c = 30.0432033439173 approximately<BR>\n" );
document.write( "c = 30.0\r<BR>\n" );
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document.write( "The fully solved triangle is<BR>\n" );
document.write( "<font color=red>𝛼 = 36°<BR>\n" );
document.write( "𝛽 = 82°<BR>\n" );
document.write( "𝛾 = 62°<BR>\n" );
document.write( "a = 20<BR>\n" );
document.write( "b = 33.7<BR>\n" );
document.write( "c = 30.0</font><BR>\n" );
document.write( "Diagram<BR>\n" );
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document.write( "Only one unique triangle is possible due to the AAS congruence theorem.<BR>\n" );
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