document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120894>Question 1120894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The figure shows a triangle STU where TU=11cm. H lies on TU such that the length of TH is 120% of the length of HU and angle SHU=90degree. Given that the area of triangle STH is 21cm^2, find angle TSU. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736672 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=736672\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your triangle looks like this:\r<BR>\n" );
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document.write( "TU = 11 cm.\r<BR>\n" );
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document.write( "TH = 120% of HU.\r<BR>\n" );
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document.write( "if we let x = HU, then 1.2x = TH\r<BR>\n" );
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document.write( "TH + TU = 11 results in 1.2x + x = 11 which results in 2.2x = 11.\r<BR>\n" );
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document.write( "solve for x to get x = 11/2.2 = 5\r<BR>\n" );
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document.write( "that makes 1.2x = 1.2 * 5 = 6\r<BR>\n" );
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document.write( "since 1.2x = TH, we have TH = 6 and we have HU = 5.\r<BR>\n" );
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document.write( "the area of triangle STH is equal to 21 cm^2.\r<BR>\n" );
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document.write( "area of a triangle is equal to 1/2 * base * height.\r<BR>\n" );
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document.write( "the area is 21 and the base is 6.\r<BR>\n" );
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document.write( "formula becomes 21 = 1/2 * 6 * H, where H is equal to SH.\r<BR>\n" );
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document.write( "solve for H to get H = 21 * 2 / 6 = 7.\r<BR>\n" );
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document.write( "the height of the triangle is equal to SH which is equal to 7.\r<BR>\n" );
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document.write( "we are looking for the measure of angle TSU.\r<BR>\n" );
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document.write( "the measure of angle TSH is equal to arctan(TH / SH which is equal to arctan(6/7).\r<BR>\n" );
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document.write( "that makes angle TSH equal to 40.60129465 degrees.\r<BR>\n" );
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document.write( "the measure of angle HSU is equal to arctan(HU/SH) which is equal to arctan(5/7).\r<BR>\n" );
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document.write( "that makes angle HSU equal to 35.53767779.\r<BR>\n" );
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document.write( "angle TSU is the sum of these two angle.\r<BR>\n" );
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document.write( "that makes angle TSU equal to 40.60129465 + 35.5376777 = 76.13897244 degrees.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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