(Trignometry, need help please.) A dog is tethered to a 14 foot leash. She travels around an arc of 49 feet. What is the radian
angle she has rotated through? (Reporting bots.)
1 answer:
Element of Circle
the central angle (α) = (the length of the arc x 360°)/2πr (r = radius)
![\alpha =\dfrac{49\times 360^o}{2\pi\times 14}=200.64^o](https://tex.z-dn.net/?f=%5Calpha%20%3D%5Cdfrac%7B49%5Ctimes%20360%5Eo%7D%7B2%5Cpi%5Ctimes%2014%7D%3D200.64%5Eo)
convert to rad:
![\tt 1^o=\dfrac{\pi}{180^o}rad\\\\200^o=\dfrac{200^o\pi}{180^0}rad=\boxed{\bold{3.48~rad}}](https://tex.z-dn.net/?f=%5Ctt%201%5Eo%3D%5Cdfrac%7B%5Cpi%7D%7B180%5Eo%7Drad%5C%5C%5C%5C200%5Eo%3D%5Cdfrac%7B200%5Eo%5Cpi%7D%7B180%5E0%7Drad%3D%5Cboxed%7B%5Cbold%7B3.48~rad%7D%7D)
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