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Use the given dimensions to find the length of each circular arc. (Round your answers to two decimal places.)

(a)  a = 60,

C = 42 cm
 _____cm 

(b) a = 72,

r = 6 ft

_______ ft 

(c) C = 56 in

______in 

(d) 5 m

______m

 Sep 4, 2018
 #1
avatar+100516 
+1

(a)  central angle  = 60....circumference  = 42 cm

 

Formula for arc length =    2 * pi * radius  * (central angle / 360 )

     42   =   2 * pi * radius * (60 / 360)

     42   =   2 * pi * radius (1/6)

     42  =  pi / 3 * radius      ......multiply both sides by  3 /pi

     42* 3 /pi   = radius  ≈  40.11 cm

 

b)  central angle  = 72........radius  = 6 ft

   

Arc length =   2 pi * 6 * ( 72 /  360)   =  12 pi *  (1/5)  = 12 / 5 * pi  ft  ≈  7.54 ft

 

 

cool cool cool

 Sep 4, 2018
 #2
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+1

What about C and D 

Guest Sep 4, 2018
 #3
avatar+100516 
+1

(c)

 

56  = 2 pi  * radius *  (145 / 360)

 

56 = 2 pi * radius*  (29/72)

 

56 =  pi * radius * (29/ 36)

 

56 = (29/36) pi  * radius      ..divide both sides by  (29/36) pi

 

56/  [ 29/36 * pi ]   =  radius  ≈ 22.13  in

 

 

 

(d)

 

Arc Length =  2 pi * 5  *  (150 /360)  =   10 (5/12) * pi    =  (5/6) * 5 pi  ≈  13.09 m

 

 

cool cool cool

 Sep 4, 2018
 #4
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C and A is wrong 

Guest Sep 4, 2018

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