document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138025>Question 1138025</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of triangle PQR is 18.  If p = 6 and q = 8, find all possible measures of angle R.  Round your answers to the nearest tenth. Show the equation used. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755904 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=755904\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "Area of triangle = 0.5*side1*side2*sin(angle)<BR>\n" );
document.write( "The \"angle\" is between side1 and side2<BR>\n" );
document.write( "Your book may refer to this as the SAS, or side-angle-side, triangle area formula.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In this case,<BR>\n" );
document.write( "area = 18<BR>\n" );
document.write( "side1 = p = 6<BR>\n" );
document.write( "side2 = q = 8<BR>\n" );
document.write( "angle = R = unknown\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's use this to solve for R<BR>\n" );
document.write( "Area of triangle = 0.5*side1*side2*sin(angle)<BR>\n" );
document.write( "Area of triangle = 0.5*p*q*sin(R)<BR>\n" );
document.write( "18 = 0.5*p*q*sin(R)<BR>\n" );
document.write( "18 = 0.5*6*8*sin(R)<BR>\n" );
document.write( "18 = 24*sin(R)<BR>\n" );
document.write( "24*sin(R) = 18<BR>\n" );
document.write( "sin(R) = 18/24<BR>\n" );
document.write( "sin(R) = 0.75<BR>\n" );
document.write( "R = arcsin(0.75) or R = 180 - arcsin(0.75)<BR>\n" );
document.write( "R = 48.590378 or R = 180 - 48.590378<BR>\n" );
document.write( "R = 48.590378 or R = 131.409622<BR>\n" );
document.write( "R = 48.6 or R = 131.4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The angle R could be either <font color=red>R = 48.6 degrees or R = 131.4 degrees</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "As a check, let's plug in p = 6, q = 8, R = 48.6<BR>\n" );
document.write( "Area of triangle = 0.5*p*q*sin(R)<BR>\n" );
document.write( "Area of triangle = 0.5*6*8*sin(48.6)<BR>\n" );
document.write( "Area of triangle = 18.002666<BR>\n" );
document.write( "which is off a bit, but keep in mind that rounding error has occurred. If we used a more accurate value of R (say something like R = 48.590378), then we would be much closer to area = 18. However, we're close enough to effectively verify this value of R.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's also check the other angle as well<BR>\n" );
document.write( "Plug in p = 6, q = 8, R = 131.4<BR>\n" );
document.write( "Area of triangle = 0.5*p*q*sin(R)<BR>\n" );
document.write( "Area of triangle = 0.5*6*8*sin(131.4)<BR>\n" );
document.write( "Area of triangle = 18.002666<BR>\n" );
document.write( "The same issue pops up as before.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );