document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=456470>Question 456470</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm pretty sure that trigonometry is needed for this problem, but I'm not totally sure!\r<BR>\n" );
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document.write( "The line 3y+x=10 intersects the circle x^2+y^2=50 in two distinct points. Suppose you drew a radius to each of the two points of intersection. Find the angle, in standard position, created by each radius.\r<BR>\n" );
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document.write( "Thank you!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #313288 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=313288\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The line 3y+x=10 intersects the circle x^2+y^2=50 in two distinct points. Suppose you drew a radius to each of the two points of intersection. Find the angle, in standard position, created by each radius.<BR>\n" );
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document.write( "Finding points of intersection<BR>\n" );
document.write( "3y+x=10<BR>\n" );
document.write( "x=10-3y<BR>\n" );
document.write( "x^2+y^2=50<BR>\n" );
document.write( "(10-3y)^2+y^2=50<BR>\n" );
document.write( "100-60y+9y^2+y^2=50<BR>\n" );
document.write( "100-60y+10y^2=50<BR>\n" );
document.write( "divide by 10<BR>\n" );
document.write( "10-6y+y^2=5<BR>\n" );
document.write( "y^2-6y+5=0<BR>\n" );
document.write( "(y-5)(y-1)=0<BR>\n" );
document.write( "y=5<BR>\n" );
document.write( "x=10-3y=10-15=-5<BR>\n" );
document.write( "y=1<BR>\n" );
document.write( "x=10-3y=10-3=7<BR>\n" );
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document.write( "Points of intersection: (-5,5) and (7,1)<BR>\n" );
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document.write( "y=(50-x^2)^.5<BR>\n" );
document.write( "y=-x/3+10/3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%2850-x%5E2%29%5E.5%2C-%2850-x%5E2%29%5E.5%2C-x%2F3%2B10%2F3%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you draw a line joining the center with the points of intersection, you will get two reference angles.<BR>\n" );
document.write( "The tangent of the reference angle on the right is 1/7.  Taking the inverse tan of 1/7=8.13º. At the other point, the inverse tan=5/5=1=45º. The angle in standard position is 180-8.13-45=126.87º </SPAN>\n" );
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