document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=443396>Question 443396</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What value of x in the interval 0° &#8804; x &#8804; 180° satisfies the equation sqrt3 tan x + 1 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305828 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305828\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29+%2A+tan%28x%29+%2B1+=+0 ALIGN=MIDDLE  ALT=\"sqrt%283%29+%2A+tan%28x%29+%2B1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29+%2Atan%28x%29+=+-1 ALIGN=MIDDLE  ALT=\"sqrt%283%29+%2Atan%28x%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29+=+%28-1%2Fsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"tan%28x%29+=+%28-1%2Fsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Where is tangent negative? In quadrants 2 and 4.\r<BR>\n" );
document.write( "\n" );
document.write( "But we are restricted to quadrants 1 and 2, since 0 < x < 180.\r<BR>\n" );
document.write( "\n" );
document.write( "Then our angle must be in quadrant 2. \r<BR>\n" );
document.write( "\n" );
document.write( "set up a 30,60,90 triangle.\r<BR>\n" );
document.write( "\n" );
document.write( "The side opposite angle 30 is 1.<BR>\n" );
document.write( "The side opposite angle 60 is sqrt(3)<BR>\n" );
document.write( "The hypotenuse is 2.\r<BR>\n" );
document.write( "\n" );
document.write( "So tangent is defined as opp/adj.  So find where our opposite is 1.  That's at angle 30.<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "Now remember we are in quadrant 2.\r<BR>\n" );
document.write( "\n" );
document.write( "So we need to create a reference angle.<BR>\n" );
document.write( "=========<BR>\n" );
document.write( "Reference angles are only based off of those that lie on the x-axis.\r<BR>\n" );
document.write( "\n" );
document.write( "That's 0, 180, 360....etc.\r<BR>\n" );
document.write( "\n" );
document.write( "Since 90 < x <180, 180 is what we will base our reference angle from.\r<BR>\n" );
document.write( "\n" );
document.write( "Take 180 and subtract 30 (our reference angle) to get 150.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28150%29 ALIGN=MIDDLE  ALT=\"highlight%28150%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our answer.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );