document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190326>Question 1190326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A quadrilateral PQRS has PQ = 18, QR = 50, RS = 45 and diagonal QS = 30. If QS bisects the angle at Q, what is the length of PS? </SPAN>\n" );
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document.write( "Let 2x be the measure of the angle that is bisected; so the measures of angles PQS and RQS are each x.  Then<br><BR>\n" );
document.write( "Using the law of cosines on triangle QRS,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%5E2=50%5E2%2B30%5E2-2%2850%29%2830%29cos%28x%29 ALIGN=MIDDLE  ALT=\"45%5E2=50%5E2%2B30%5E2-2%2850%29%2830%29cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > [1]<br><BR>\n" );
document.write( "Using the law of cosines on triangle PQS,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=18%5E2%2B30%5E2-2%2818%29%2830%29cos%28x%29 ALIGN=MIDDLE  ALT=\"x%5E2=18%5E2%2B30%5E2-2%2818%29%2830%29cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > [2]<br><BR>\n" );
document.write( "Solve [1] for cos(x) and substitute in [2].<br><BR>\n" );
document.write( "I'll leave it to you to do the calculations....<br><BR>\n" );
document.write( "If you only want the answer, without a chance to learn something from working on the problem, the answer is PS=27.<br><BR>\n" );
document.write( " </SPAN>\n" );
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