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  • secretliker
    secretliker's Avatar
    255 posts since Dec '06
  • FirePig
    FirePig's Avatar
    1,183 posts since Mar '08
    • 13 Apr `08, 12:22AM

      Use opp angles of cyclic quad, use adjacent angles on straight line, cosine rule maybe, sine rule

       

      find area of sector (1/2r^2theta*0.7/2pi) - area of triangle Area(a*b*sin(C)/2)...

       

      I will leave the details another day. You go try first. 

      Edited by FirePig 13 Apr `08, 12:25AM
  • Moderator
    eagle
    eagle's Avatar
    17,967 posts since Aug '01
    • 13 Apr `08, 12:43AM

      a)
      angle abc = pi - 1.38 rad

      using sine rule,

      AB/sin0.7 = 10/sin(pi-1.38)
      AB = 6.56cm

       

      b) angle oab = pi - (0.7) - (pi-1.38) = 0.68 rad
      area of shaded area = area of sector - area of unshaded triangle

      = 1/2 (10^2) (0.7) - 1/2 (10)(6.56)sin(0.68)
      = 35 - 20.6244
      =14.4 cm^2

  • secretliker
    secretliker's Avatar
    255 posts since Dec '06
    • 13 Apr `08, 12:57AM

      Thanks eagle. but part b first line should be:

      angle OAB = pi - angle AOB - angle ABO = pi - 0.7 - 1.38 = 1.06159 rad

  • weiwei
    weiwei's Avatar
    330 posts since Oct '01
    • 15 Apr `08, 10:58AM
      Originally posted by eagle:

      a)
      angle abc = pi - 1.38 rad

      using sine rule,

      AB/sin0.7 = 10/sin(pi-1.38)
      AB = 6.56cm

       

      b) angle oab = pi - (0.7) - (pi-1.38) = 0.68 rad
      area of shaded area = area of sector - area of unshaded triangle

      = 1/2 (10^2) (0.7) - 1/2 (10)(6.56)sin(0.68)
      = 35 - 20.6244
      =14.4 cm^2

      eagle, think there's a minor typo in part (a) leh.

      using sine rule,

      AB/sin0.7 = 10/sin1.38

      your answer correct >.<

  • Moderator
    eagle
    eagle's Avatar
    17,967 posts since Aug '01
    • 15 Apr `08, 11:05AM
      Originally posted by weiwei:

      eagle, think there's a minor typo in part (a) leh.

      using sine rule,

      AB/sin0.7 = 10/sin1.38

      your answer correct >.<

      yup TS has already pointed out... He's a good self-learner... thumbs_up.png

      the answer appears correct because sin(1.38) gives the same value as sin(pi - 1.38)

       

       

      Edited by eagle 15 Apr `08, 11:06AM
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