document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=957691>Question 957691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is Applications of Trigonometry, that involves the law of sines. I can't figure out the diagram. After that I would know what to do.\r<BR>\n" );
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document.write( "A huge mound of dirt is near a construction site. Andrew wants to find out how high the mound is. He measures the angle to the top of the mound to be 57 degrees. Then he walks 8 feet away from the base of the mound and measures the angle to the top of the mound again to be 35 degrees. To the nearest tenth of a foot, what is the height of the mound? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #585315 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=585315\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your diagram is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/032303.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the height of your mound is h.<BR>\n" );
document.write( "the distance between the center of the mound and the 57 degree angle is x.<BR>\n" );
document.write( "the distance between the center of the mound and the 35 degree angle is x + 8.\r<BR>\n" );
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document.write( "tan(57) = h/x\r<BR>\n" );
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document.write( "tan(35) = h/(x+8)\r<BR>\n" );
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document.write( "solve for x in these equations to get:\r<BR>\n" );
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document.write( "x = h / tan(57)\r<BR>\n" );
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document.write( "x = h / tan(35) - 8\r<BR>\n" );
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document.write( "replace x with h / tan(57) in the second equation to get:\r<BR>\n" );
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document.write( "h / tan(57) = h / tan(35) - 8\r<BR>\n" );
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document.write( "solve for h in this equation to get h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-8+%2A+tan%2835%29+%2A+tan%2857%29%29+%2F+%28tan%2835%29+-+tan%2857%29%29 ALIGN=MIDDLE  ALT=\"%28-8+%2A+tan%2835%29+%2A+tan%2857%29%29+%2F+%28tan%2835%29+-+tan%2857%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "i'm assuming you know how to solve for h in that equation.<BR>\n" );
document.write( "if you don't, let me know and i'll step you through it.\r<BR>\n" );
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document.write( "the equation of h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-8+%2A+tan%2835%29+%2A+tan%2857%29%29+%2F+%28tan%2835%29+-+tan%2857%29%29 ALIGN=MIDDLE  ALT=\"%28-8+%2A+tan%2835%29+%2A+tan%2857%29%29+%2F+%28tan%2835%29+-+tan%2857%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > gets you h = 10.27299966.\r<BR>\n" );
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document.write( "now that you know h, you can solve for x.\r<BR>\n" );
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document.write( "tan(57) = h/x is the equation you start with.\r<BR>\n" );
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document.write( "solve for x in this equation to get x = h / tan(57).\r<BR>\n" );
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document.write( "use the value of h you just solved for to get x = 10.27299966 / tan(57) which results in x = 6.671363981.\r<BR>\n" );
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document.write( "you can now confirm that your answer for h is correct.\r<BR>\n" );
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document.write( "tan(57) = h/x becomes tan(57) = 10.27299966 / 6.671363981 which becomes tan(57) = 1.539864964.\r<BR>\n" );
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document.write( "use your calculator to find tan(57) = 1.539864964.\r<BR>\n" );
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document.write( "since they're the same, your value of h and x is good for tan(57).\r<BR>\n" );
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document.write( "x + 8 is equal to 6.671363981 + 8 which is equal to 14.671363981.\r<BR>\n" );
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document.write( "tan(35) = h / (x+8) becomes tan(35) = 10.27299966 / 14.671363981 which becomes tan(35) = .7002075382.\r<BR>\n" );
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document.write( "use your calculator to find tan(35) = .7002075382.\r<BR>\n" );
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document.write( "since they're the same, your value of h and (x+8) is good for tan(35).\r<BR>\n" );
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document.write( "the height of your mound is 10.27299966 feet which rounds to 10.3 feet.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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