Length of an Arc

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This item is taken from IGCSE Mathematics (0580) Paper 43 (Extended) of June 2013.

To deal with this item, let us summarize the details of the problem:
   (a) Syllabus area: Trigonometry
   (b) Specific topic: Length of an Arc
   (c) Formula Needed: 
sectors,IGCSE,geometry,mathematics,examination,Cambridge,circles,radius
It is given that the central angle subtended by the arc (fence) measures 210 degrees. The illustration/photo below shows the sector enclosed by the fence and the central angle.
sectors,IGCSE,geometry,mathematics,examination,Cambridge,circles,radius
Using the values given,
sectors,IGCSE,geometry,mathematics,examination,Cambridge,circles,radius
Therefore, the length of the fence is 165 m.

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