document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087786>Question 1087786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hey guys I been trying to solve this question but I just don't get it<BR>\n" );
document.write( "The question is;\r<BR>\n" );
document.write( "\n" );
document.write( "In constructing a triangle, the direction were to make one angle 40° with its opposite side 15 cm and an adjacent side 18 cm long. What are the possible measurements for the third side?\r<BR>\n" );
document.write( "\n" );
document.write( "Your help will be very much appreciated, THANK YOU  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #702070 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=702070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">Let,<BR>\n" );
document.write( "angle A = 40 degrees<BR>\n" );
document.write( "side a = 15 cm (side a is opposite angle A)<BR>\n" );
document.write( "side b = 18 cm (adjacent to side a)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The ultimate goal is to find the length of side c.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's use the law of sines to find angle B\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sin(A)/a = sin(B)/b<BR>\n" );
document.write( "sin(40)/15 = sin(B)/18<BR>\n" );
document.write( "0.042852507312436 = sin(B)/18<BR>\n" );
document.write( "18*0.042852507312436 = 18*sin(B)/18<BR>\n" );
document.write( "0.771345131623847 = sin(B)<BR>\n" );
document.write( "sin(B) = 0.771345131623847<BR>\n" );
document.write( "arcsin(sin(B)) = arcsin(0.771345131623847)<BR>\n" );
document.write( "B = arcsin(0.771345131623847) ... or ... B = 180 - arcsin(0.771345131623847)<BR>\n" );
document.write( "B = 50.4748346316044 ... or ... B = 129.525165368396<BR>\n" );
document.write( "B = 50.47 ... or ... B = 129.53<BR>\n" );
document.write( "I'm rounding to two decimal places to make future calculations a bit simpler (and not as cluttered)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If angle B = 50.47, then angle C = 180-A-B = 180-40-50.47 = 89.53<BR>\n" );
document.write( "If angle B = 129.53, then angle C = 180-A-B = 180-40-129.53 = 10.47\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In summary so far, we have two sets of angles\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first set of angles is<BR>\n" );
document.write( "angle A = 40 degrees, angle B = 50.47 degrees (approximate), angle C = 89.53 degrees (approximate)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The other set of angles is <BR>\n" );
document.write( "angle A = 40 degrees, angle B = 129.53 degrees (approximate), angle C = 10.47 degrees (approximate)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's focus on the first set of angles<BR>\n" );
document.write( "angle A = 40<BR>\n" );
document.write( "angle B = 50.47<BR>\n" );
document.write( "angle C = 89.53<BR>\n" );
document.write( "we can use these angles, along with the sides a = 15 and b = 18, to find the third side c\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the law of cosines to find the value for c<BR>\n" );
document.write( "c^2 = a^2 + b^2 - 2*a*b*cos(C)<BR>\n" );
document.write( "c^2 = (15)^2 + (18)^2 - 2*(15)*(18)*cos(89.53)<BR>\n" );
document.write( "c^2 = 544.570404036738<BR>\n" );
document.write( "c = sqrt(544.570404036738)<BR>\n" );
document.write( "c = 23.3360323113579<BR>\n" );
document.write( "c = 23.34\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So one possible length for the missing side is approximately 23.34 cm\r<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "Now focus on the other set of angles <BR>\n" );
document.write( "angle A = 40<BR>\n" );
document.write( "angle B = 129.53 <BR>\n" );
document.write( "angle C = 10.47<BR>\n" );
document.write( "we'll use these angles along with a = 15 and b = 18. Solve for c\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c^2 = a^2 + b^2 - 2*a*b*cos(C)<BR>\n" );
document.write( "c^2 = (15)^2 + (18)^2 - 2*(15)*(18)*cos(10.47)<BR>\n" );
document.write( "c^2 = 17.9908968194146<BR>\n" );
document.write( "c = sqrt(17.9908968194146)<BR>\n" );
document.write( "c = 4.24156773132466<BR>\n" );
document.write( "c = 4.24\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The other possible length for the missing side is 4.24 cm\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The third missing side is either approximately equal to 23.34 cm or 4.24 cm\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Keep in mind that I rounded things to 2 decimal places to keep things simple. Use more decimal digits to get better accuracy.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here is a look at the two solutions side by side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/zGHpCW9.png\"><BR>\n" );
document.write( "(Image generated by <a  rel=nofollow HREF= \"https://www.geogebra.org/home?ggbLang=en\">GeoGebra</a> which is free graphing software)\r<BR>\n" );
document.write( "\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );