document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1073781>Question 1073781</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diameter of the earth’s orbit around the sun is approximately 186 million miles.<BR>\n" );
document.write( "Looking at a star from the two points on the orbit which are furthest apart, the lines of sight<BR>\n" );
document.write( "to the star form an angle of 4.269 × 10&#8722;4 degrees. How many light-years away is this star<BR>\n" );
document.write( "from the earth? Note that one light-year is approximately 5.879 × 1012 miles. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688711 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=688711\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  The diameter of the earth’s orbit around the sun is approximately 186 million miles. 1.86(10^8)<BR>\n" );
document.write( " Looking at a star from the two points on the orbit which are furthest apart, the lines of sight  to the star form an angle of 4.269 × 10^-4 degrees.<BR>\n" );
document.write( " How many light-years away is this star  from the earth?<BR>\n" );
document.write( " Note that one light-year is approximately 5.879 × 10^12 miles.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let d = distance from the earth to the star<BR>\n" );
document.write( "Utilize a right triangle formed from the center of the orbit to a point on the orbit to the star.<BR>\n" );
document.write( "Use half the given angle: 2.1345(10^-4) degrees<BR>\n" );
document.write( "Use half the diameter of the orbit as the side opposite, 9.3(10^7) miles<BR>\n" );
document.write( "Use the sine of the angle to find d (hypotenuse}<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282.1345%2810%5E-4%29%29+=+9.3%2810%5E7%29%2Fd ALIGN=MIDDLE  ALT=\"sin%282.1345%2810%5E-4%29%29+=+9.3%2810%5E7%29%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+9.3%2810%5E7%29%2Fsin%282.1345%2810%5E-4%29%29 ALIGN=MIDDLE  ALT=\"d+=+9.3%2810%5E7%29%2Fsin%282.1345%2810%5E-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the calc<BR>\n" );
document.write( "d = 2.496(10^13) miles<BR>\n" );
document.write( "Change to light years<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.496%2810%5E13%29%2F5.879%2810%5E12%29 ALIGN=MIDDLE  ALT=\"2.496%2810%5E13%29%2F5.879%2810%5E12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =  .425(10) = 4.25 light years   </SPAN>\n" );
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