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find the length of an arc of a circle of radius 12ft if the arc subtends a central angle of 135

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2 Answers

s=rθ  (where θ is given in radians)
135º = 135º (π/180º) = 3π/4 radians  (reducing the factor of 45 in the top and bottom)
                                                                    (recall: π/180º=1)
s=(12 ft)(3π/4)
 = (3 ft)(3π)    (dividing 12 by 4)
 = 9π ft
the circumference will measure 2*π *r= 24π then if the circumference is 360 degrees, which will be the arc for 135 degrees?
24π *(135/360) = 9π this is the length of the arc.o or 3.141592* 9 = 28.27 ft


Careful about setting π "equal" to any finite decimal representation (pure mathematicians may get upset ;)