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

Question

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

Answer 1

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

Answer 2

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