document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201909>Question 1201909</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Don't understand how the answer to this problem is 15.\r<BR>\n" );
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document.write( "csc(arctan(square root 14/56)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836484 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=836484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "sqrt = \"square root\"<BR>\n" );
document.write( "example: sqrt(7) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%29 ALIGN=MIDDLE  ALT=\"sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > = theta = arctan(sqrt(14)/56)<BR>\n" );
document.write( "This leads to tan(theta) = sqrt(14)/56\r<BR>\n" );
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document.write( "Recall that tangent is the ratio opposite/adjacent.\r<BR>\n" );
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document.write( "tan(theta) = sqrt(14)/56<BR>\n" );
document.write( "tan(theta) = opposite/adjacent<BR>\n" );
document.write( "opposite = sqrt(14)<BR>\n" );
document.write( "adjacent = 56\r<BR>\n" );
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document.write( "Let's draw a right triangle with these properties.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28300%2C300%2C-5%2C5%2C-6%2C4%2C%0D%0Aline%283%2C3%2C3%2C-3%29%2C%0D%0Aline%283%2C-3%2C-3%2C-3%29%2C%0D%0Aline%28-3%2C-3%2C3%2C3%29%2C%0D%0Alocate%283.1%2C0.5%2C%22opposite%22%29%2C%0D%0Alocate%283.1%2C0%2Csqrt%2814%29%29%2C%0D%0Alocate%28-1%2C-3.2%2C%22adjacent%22%29%2C%0D%0Alocate%28-0.2%2C-3.7%2C56%29%2C%0D%0Alocate%28-2%2C1.2%2C%22hypotenuse%22%29%2Clocate%28-1%2C0.5%2C%22x%22%29%2C%0D%0Alocate%28-1.8%2C-2.1%2Ctheta%29%2C%0D%0Alocate%28-4%2C-5%2Cmatrix%281%2C4%2CDiagram%2Cnot%2Cto%2Cscale%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = hypotenuse\r<BR>\n" );
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document.write( "Use the pythagorean theorem to find x.<BR>\n" );
document.write( "a^2+b^2 = c^2<BR>\n" );
document.write( "(sqrt(14))^2+56^2 = x^2<BR>\n" );
document.write( "14+3136 = x^2<BR>\n" );
document.write( "3150 = x^2<BR>\n" );
document.write( "x^2 = 3150<BR>\n" );
document.write( "x = sqrt(3150)<BR>\n" );
document.write( "x = sqrt(225*14)<BR>\n" );
document.write( "x = sqrt(225)*sqrt(14)<BR>\n" );
document.write( "x = 15*sqrt(14)\r<BR>\n" );
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document.write( "Let's update the diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28300%2C300%2C-5%2C5%2C-6%2C4%2C%0D%0Aline%283%2C3%2C3%2C-3%29%2C%0D%0Aline%283%2C-3%2C-3%2C-3%29%2C%0D%0Aline%28-3%2C-3%2C3%2C3%29%2C%0D%0Alocate%283.1%2C0.5%2C%22opposite%22%29%2C%0D%0Alocate%283.1%2C0%2Csqrt%2814%29%29%2C%0D%0Alocate%28-1%2C-3.2%2C%22adjacent%22%29%2C%0D%0Alocate%28-0.2%2C-3.7%2C56%29%2C%0D%0Alocate%28-2%2C1.2%2C%22hypotenuse%22%29%2Clocate%28-1.8%2C0.5%2C15%2Asqrt%2814%29%29%2C%0D%0Alocate%28-1.8%2C-2.1%2Ctheta%29%2C%0D%0Alocate%28-4%2C-5%2Cmatrix%281%2C4%2CDiagram%2Cnot%2Cto%2Cscale%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%28theta%29+=+hypotenuse%2Fopposite ALIGN=MIDDLE  ALT=\"csc%28theta%29+=+hypotenuse%2Fopposite\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%28theta%29+=+%2815%2Asqrt%2814%29%29%2F%28sqrt%2814%29%29 ALIGN=MIDDLE  ALT=\"csc%28theta%29+=+%2815%2Asqrt%2814%29%29%2F%28sqrt%2814%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%28theta%29+=+%2815%2Ahighlight%28sqrt%2814%29%29%29%2F%28highlight%28sqrt%2814%29%29%29 ALIGN=MIDDLE  ALT=\"csc%28theta%29+=+%2815%2Ahighlight%28sqrt%2814%29%29%29%2F%28highlight%28sqrt%2814%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%28theta%29+=+%2815%2Across%28sqrt%2814%29%29%29%2F%28cross%28sqrt%2814%29%29%29 ALIGN=MIDDLE  ALT=\"csc%28theta%29+=+%2815%2Across%28sqrt%2814%29%29%29%2F%28cross%28sqrt%2814%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%28theta%29+=+15 ALIGN=MIDDLE  ALT=\"csc%28theta%29+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%28arctan%28sqrt%2814%29%2F56%29%29+=+15 ALIGN=MIDDLE  ALT=\"csc%28arctan%28sqrt%2814%29%2F56%29%29+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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