Question 564119
The circumference is {{{ 2*pi*2 = 4*pi }}} cm
The ratio of ( arc in radians ) / ( 2pi ) = ( 3 cm ) / ( 4pi )
{{{ r / (2*pi) = 3 / (4*pi) }}}
Multiply both sides by {{{ 4*pi }}}
{{{ 2r = 3 }}}
{{{ r = 2/3 }}} radians
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I can say:
{{{ ( 2/3 ) / pi = d / 180  }}}
Multiply both sides by {{{ 180*pi }}}
{{{ (2/3)*180 = d*pi }}}
{{{ 120 = d*pi }}}
{{{ d = 120/pi }}}
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The arc is 2/3 radians or 120/pi degrees
check:
{{{ ( 120/pi ) / 360 = (2/3) / ( 2*pi ) }}}
Multiply both sides by {{{ 360*pi }}}
{{{ 120 = (2/3)*180 }}}
{{{ 120 = 120 }}}
OK