document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=343975>Question 343975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In triangle ABC, C = 60 degrees, a = 12, and b= 5. Find c.\r<BR>\n" );
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document.write( "a. 109.0<BR>\n" );
document.write( "b. 10.4<BR>\n" );
document.write( "c. 11.8<BR>\n" );
document.write( "d. 15.1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #246087 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=246087\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In triangle ABC, C = 60 degrees, a = 12, and b= 5. Find c. <BR>\n" );
document.write( "a. 109.0<BR>\n" );
document.write( "b. 10.4<BR>\n" );
document.write( "c. 11.8<BR>\n" );
document.write( "d. 15.1\r<BR>\n" );
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document.write( "are a and b 2 of the sides?\r<BR>\n" );
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document.write( "is c one of the sides?\r<BR>\n" );
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document.write( "is this a right triangle?\r<BR>\n" );
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document.write( "maybe you should repost\r<BR>\n" );
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document.write( "if this is right triangle: <BR>\n" );
document.write( "then angles would be 30-60-90,<BR>\n" );
document.write( "angle C would be the 60, angle B would be the 30, angle A would be the 90,<BR>\n" );
document.write( "side c opposite angle C, side b = 5, side a = 12<BR>\n" );
document.write( "pythagorean theorem: b^2 + c^2 = a^2 --> 5^2 + c^2 = 12^2<BR>\n" );
document.write( "b^2 + c^2 = a^2 --> 5^2 + c^2 = 12^2 = c^2 + 25 = 144<BR>\n" );
document.write( "c^2 = 119<BR>\n" );
document.write( "c = sqrt(119) = 10.9087 to 4 places\r<BR>\n" );
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document.write( "if this is not a right triangle:<BR>\n" );
document.write( "if angle C of 60 is the side opposite, and a and b are the 2 known sides:<BR>\n" );
document.write( "use law of cosines: c^2 = a^2 + b^2 - 2abcosC<BR>\n" );
document.write( "c^2 = 12^2 + 5^2 - 2 * 12 * 5 * cos 60<BR>\n" );
document.write( "c^2 = 144 + 25 - 120cos60<BR>\n" );
document.write( "c^2 = 169 - 120 * 0.5<BR>\n" );
document.write( "c^2 = 169 - 60 = 109<BR>\n" );
document.write( "c = sqrt(109) = 10.4403 rounded to 4 places<BR>\n" );
document.write( "well this would match up with answer b. 10.4\r<BR>\n" );
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