document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=993592>Question 993592</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the shadow of a pole when the angle of elevation of the sun is 32° is 5m longer than the shadow of the pole when the angle of elevation of the sun is 48°. what is the length of the longer shadow of the pole? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #612891 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=612891\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> tan(48) = y/x\r<BR>\n" );
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document.write( "tan(32) = y/(x+5)\r<BR>\n" );
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document.write( "solve for y in both equation to get:\r<BR>\n" );
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document.write( "y = x * tan(48)\r<BR>\n" );
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document.write( "y = (x+5) * tan(32)\r<BR>\n" );
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document.write( "since they're both equal to y, the expressions on the right side of each equation must be equal to each other, so:\r<BR>\n" );
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document.write( "x * tan(48) = (x + 5) * tan(32)\r<BR>\n" );
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document.write( "simplify the right side of the equation to get:\r<BR>\n" );
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document.write( "x * tan(48) = x * tan(32) + 5 * tan(32)\r<BR>\n" );
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document.write( "subtract x * tan(32) from both sides of the equation to get:\r<BR>\n" );
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document.write( "x * tan(48) - x * tan(32) = 5 * tan(32)\r<BR>\n" );
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document.write( "simplify the left side of the equation to get:\r<BR>\n" );
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document.write( "x * (tan(48) - tan(32)) = 5 * tan(32)\r<BR>\n" );
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document.write( "divide both sides of the equation by (tan(48) - tan(32)) to get:\r<BR>\n" );
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document.write( "x = (5 * tan(32)) / (tan(48) - tan(32))\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 6.432096215\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "x + 5 must therefore be equal to 11.432096215\r<BR>\n" );
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document.write( "now that you know the value of x and x + 5, you can use that information to solve for y.\r<BR>\n" );
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document.write( "it should be the same in both cases.\r<BR>\n" );
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document.write( "if y = x * tan(48), then y is equal to 6.432096215 * tan(48) which is equal to 7.143566553.\r<BR>\n" );
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document.write( "if y = (x + 5) * tan(32), y is equal to 11.43209621 * tan(32) which is equal to 7.143566553.\r<BR>\n" );
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document.write( "y is the same in both cases, as it should be.\r<BR>\n" );
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document.write( "your solution is that the length of the longer shadow of the pole is 6.432096215 + 5 = 11.432096215\r<BR>\n" );
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document.write( " </SPAN>\n" );
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