F3 Maths question!

左三角形ABC中,已知sin(A/2)=(sqrt5)/3

求sin((B+C)/2)的值

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Please construct a triangle if it is possible!

更新:

Wrong!

更新 2:

The answer is 2/3..

3 個解答

評分
  • 10 年前
    最愛解答

    Correct answer as follows:

    sin [ ( B + C ) / 2 ]

    = sin [ ( 180 Degrees - A ) / 2 ]

    = sin [ 90 Degrees - A / 2 ]

    = cos ( A / 2 )

    = Sq Root [ 1 - sin^2 ( A/2 ) ]

    = Sq Root ( 1 - 5/9 )

    = Sq Root ( 4/9 )

    = 2/3

    =====

    Hope I can help you.

    資料來源: Mathematics Teacher Mr. Ip
  • 10 年前

    圖片參考:http://imgcld.yimg.com/8/n/HA00141790/o/7011041400...

    hope i can help u

    the last explaination is about F.4 M2 maths

    i duno if it is ok

  • 10 年前

    sin((B+C)/2)

    = sin(90 - A/2)

    = cos(A/2)

    = √(1 - sin^2 (A/2))

    or -√(1 - sin^2 (A/2)) rejected since A/2 < 90 , cos(A/2) +ve

    = √(1 - 5/9)

    = 2/3 A/2 =48.19

    A =96.38Would you mind construct a triangle with angle A=96.38 degrees

    yourself?

    2011-04-14 20:33:18 補充:

    B and C are uncertain

    資料來源: , By me
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