Sector of a circle

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    I am trying to work out the area of the shaded part of the diagram. I've figured that If I was to work out the area of the triangle (27cm) and take it away from the sector, I'd have the area of the shaded bit.

    I'm guessing that I'd have to use trigonometory to find the area of the sector, I really have no idea how to do this, and would appreciate some help. Thankyou
     
    Last edited: Dec 6, 2007
  2. jcsd
  3. chroot

    chroot 10,426
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    You're on the right track.

    You know the area of the entire circle; it's pi times the radius squared.

    You also know what fraction of that area is included in the sector; it's x/360, where x is in degrees.

    - Warren
     
    Last edited: Dec 7, 2007
  4. Thanks for your help
    But how would I work out the size of angle X. Would cos, sin or tan have to be used?
     
  5. chroot

    chroot 10,426
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    You know all three sides -- use the law of cosines to find the angles.

    - Warren
     
  6. robphy

    robphy 4,416
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    Less elegantly, you can break the triangle into two congruent right-triangles... then apply trigonometry with a right-triangle.
     
  7. Are you sure that the area of the triangle is 27cm?
     
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