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Math Help - Length of sides and angle calculations

  1. #1
    Junior Member
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    Length of sides and angle calculations

    Hi,

    Can someone tell me how I would find a) the length of side BC and

    b) the angle B,on the sketch,

    Thanks....
    Attached Thumbnails Attached Thumbnails Length of sides and angle calculations-01-02-2010-12-45-26_0063.jpg  
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  2. #2
    Super Member

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    Hello, manich44!

    Is there more information?
    As given, the problem has no single solution.
    Code:
                    D
                    o
                  *   *
                *       *
              *           *
            *               *
        A o  105.4           *
           *                    o C
            *
             *
              *
               *
                *
                 *
                  o
                  B

    We are given 3 sides and one angle of a quadrilateral.

    This does not determine a unique quadrilateral.

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  3. #3
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    RE

    Sorry Guys,
    Forgot to include total area = 1276m2
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  4. #4
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    Hello, manich44!

    I'll give you the Game Plan.
    The rest is up to you . . .


    Code:
                  D
                  o
         34.37  * : α *    37.62
              *   :       *
            *     :           *
        A o 105.4:               o C
           *      :             *
            *     :           *
             *    :         *
         41.4 *   :       *
               * θ:     *
                * : β *
                 *: *
                  o
                  B

    Area of ABCD \,=\,1276\text{ m}^2

    Find: . (a)\;BC,\;\;\;(b)\;\angle B

    \text{Let: }\:\theta = \angle ABD,\;\alpha = \angle BDC,\;\beta = \angle DBC


    [1] Area of \Delta ABD \,=\,\tfrac{1}{2}(41.4)(34.36)\sin105.4^o \:\approx\:686\text{ m}^2

    . . Hence: ,Area of \Delta BCD \:=\:1276 - 686 \:=\:590\text{ m}^2


    [2] We know: . AB = 41.4,\;AD = 34.37,\;\angle A = 105.4^o

    . . . Use the Law of Cosines to find BD.


    [3] We know all three sides of \Delta ABD.
    . . . Use the Law of Cosines to find \theta


    [4] Area of \Delta BCD \,=\,590\text{ m}^2

    . . . We have: . \tfrac{1}{2}(BD)(CD)\sin\alpha \:=\:590 \quad\hdots Solve for \alpha.


    [5] We know: DB,\:DC,\:\angle\alpha
    . . . Use the Law of Cosines to find side BC .(a)


    [6] We know all three sides of \Delta BCD.
    . . . Use the Law of Cosines to find \beta


    [7] Hence: . \angle B \:=\:\theta + \beta .(b)

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  5. #5
    Junior Member
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    RE

    Hi,
    Thanks for the help.
    I get length BC = 34.30 and angle B 74.6 deg.

    Thanks...
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