document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091197>Question 1091197</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many triangles can be formed if side a = 17 ft? In triangle ABC, &#61648;A = 60°, and side c = 18 ft.<BR>\n" );
document.write( "Select one:<BR>\n" );
document.write( "a. 0 <BR>\n" );
document.write( "b. 2 <BR>\n" );
document.write( "c. 3 <BR>\n" );
document.write( "d. 1  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #705835 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=705835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> d. 1    looks correct<BR>\n" );
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document.write( "Using the Law of Sines:\r<BR>\n" );
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document.write( "   sin(A)/a = sin(B)/b = sin(C)/c\r<BR>\n" );
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document.write( "Since A=60 degrees, a=17ft, and c=18ft are given, one can compute C=54.876 degrees directly and then using A+B+C = 180, angle B can be found to be 65.124 degrees.  The values given constrain the solution to one specific triangle.  <BR>\n" );
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document.write( "EDIT 8/25/17:   Yes, MathTherapy is correct, there are TWO triangles (thanks MathTherapy for pointing it out).   I made a calculation error in the computation of angle C, it should be 66.5 degrees (and hence the triangle with c=18, C=66.5 degrees is indeed valid).   More importantly, I missed sin(C) = sin(180-C) and that gives you a 2nd triangle (one triangle has A,B,C = 60, 53.5, 66.5 degrees with sides a,b,c = 17, 15.78, 18 feet, respectively.  The 2nd triangle has  A,B,C = 60, 6.5, 113.5 degrees, with sides a, b, c = 17, 2.222, 18 feet,  respectively).   I'd change that to \"answer 'b' looks correct.\"      <BR>\n" );
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