document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139849>Question 1139849</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the appropriate special triangle, determine θ if 0° ≤θ≤90° for tan θ/√3=1<BR>\n" );
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document.write( "determine θ if 0° ≤ θ ≤90° for tan (theta)/sqrt(3)=1\r<BR>\n" );
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document.write( "The special triangles:<BR>\n" );
document.write( "30-60-90 triangles<BR>\n" );
document.write( "45-45-90 triangles\r<BR>\n" );
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document.write( "the trig ratios for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30 ALIGN=MIDDLE  ALT=\"30\"   DISABLED_style= \"max-width:90%; height:auto;\" >° , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45 ALIGN=MIDDLE  ALT=\"45\"   DISABLED_style= \"max-width:90%; height:auto;\" >° , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" >° : the table below summarizes our results\r<BR>\n" );
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document.write( ".............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29 ALIGN=MIDDLE  ALT=\"tan%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30 ALIGN=MIDDLE  ALT=\"30\"   DISABLED_style= \"max-width:90%; height:auto;\" >°..........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >..............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >......................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"1%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45 ALIGN=MIDDLE  ALT=\"45\"   DISABLED_style= \"max-width:90%; height:auto;\" >°..........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >..............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" >°............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "These values tend to occur often in advanced trigonometry problems. Because of this, it is helpful to know them.\r<BR>\n" );
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document.write( "so, if you have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+%28theta%29%2Fsqrt%283%29=1 ALIGN=MIDDLE  ALT=\"tan+%28theta%29%2Fsqrt%283%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+%28theta%29=sqrt%283%29 ALIGN=MIDDLE  ALT=\"tan+%28theta%29=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "from the table you got\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=60 ALIGN=MIDDLE  ALT=\"theta=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >° => and appropriate special triangle is 30-60-90 triangle\r<BR>\n" );
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