I need a little help..Could someone help me...?

The figure below shows the ideal pattern of movement of a herd of cattle, with the arrows showing the movement of the handler as he moves the herd. The arc the handler makes from the starting point to the return point should be a quarter of a circle.

Based on this theory, what distance will the handler move from the starting point to the return point if he creates an arc of a circle of radius 80 feet?
125.6 feet
502.4 feet
83.73 feet
62.8 feet

Question

I need a little help..Could someone help me...?

 The figure below shows the ideal pattern of movement of a herd of cattle, with the arrows showing the movement of the handler as he moves the herd. The arc the handler makes from the starting point to the return point should be a quarter of a circle.
 

 
Based on this theory, what distance will the handler move from the starting point to the return point if he creates an arc of a circle of radius 80 feet?
 125.6 feet
 502.4 feet
 83.73 feet
 62.8 feet

anonymous · Answer

attachment

hartnn · Answer

Length of arc = $r \theta$
where r=radius = 80 here. 
do you know what angle $\theta $ doeas a quarter circle make ?

anonymous · Answer

90..?

anonymous · Answer

^yep

hartnn · Answer

yes, its 90 degrees :) 
do you know what is it in radians, because for that formula you need angle in radians.

anonymous · Answer

awesome!! would it be 45..? or am i completely off..? lol :D

hartnn · Answer

45 for what ? 
90 degrees angle for quarter circle was correct.
now to convert any degree angle to radian angle, just multiply it by $\pi /180$
so 90 degrees =... ? radians ?

anonymous · Answer

141.3..?

hartnn · Answer

141.3 for what ? 
what did you get for angle theta in radians ? 
90 degrees = how many pi radians ?

hartnn · Answer

once you get that, you'll just need to multiply 80 to it.

anonymous · Answer

im not sure what you mean by radians...:/

hartnn · Answer

ok, let me give some examples : 
$30^o = 30 \times \pi/180 = \pi/6 (radians) \ 60^o = 60 \times \pi/180=\pi/3 $
what about 90 degrees ?

anonymous · Answer

i'm so sorry i'm being difficult..

anonymous · Answer

so would the radian of 90 be 0.785

hartnn · Answer

oh, no problem at all, i know this is difficult to grasp in one time, but i'll need you to try once, if its incorrect, i'll point out the error...
umm, lets check, 
$90^o = 90 \times \pi/180 = \pi/2 =3.14/2 = 1.57 $
how'd you got 0.785 ? :O

hartnn · Answer

did you do pi/4 ?

anonymous · Answer

whoops lol :D i mult 90by pi divided it by 180... but that is completely WRONG!! lol :D

hartnn · Answer

' mult 90by pi divided it by 180' <---is also what i did.
you should have got 1.57 from that ...

hartnn · Answer

anyways, whats remaining part is just to multiply it with 80
Arc length = 80*1.57 =... ?

anonymous · Answer

125.6!!!!!?

hartnn · Answer

$\huge \checkmark $

anonymous · Answer

YAYAYAYAYY!!

anonymous · Answer

Thank you sooo much!!

hartnn · Answer

Welcome  sooo much!!