Question 1115066
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{{{sin(30)=1/2}}} and {{{cos(30)=sqrt(3)/2}}}

If r is the length of the guy wire  (make drawing to see everything), 
then  {{{cos(30)=6/r}}}

{{{r/6=2/sqrt(3)}}}

{{{r=12/sqrt(3)}}}

{{{r=(12/sqrt(3))(sqrt(3)/sqrt(3))}}}

{{{r=12*sqrt(3)/3}}}

{{{highlight(r=4*sqrt(3))}}}-----length of guy wire.
and Pythagorean theorem could be used for finding the height of pole...




Also recognize, the triangle formed is a special 30-60-90 right triangle.  Long leg is 6 meters.  Let x be the short leg (height of the flag pole).  The wire is then 2x.


{{{x^2+6^2=(2x)^2}}}
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{{{x^2+36=4x^2}}}
{{{3x^2=36}}}
{{{x^2=12}}}
{{{x=sqrt(2*2*3)}}}
{{{highlight(x=2*sqrt(3))}}}------height
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{{{highlight(4*sqrt(3))}}}-------guy wire