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Math Help - finding length in truss

  1. #1
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    Unhappy finding length in truss



    Find the lengths of BF and CF?

    i have found that BF is 4779 i now need to know how to find CF
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  2. #2
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    Hello, Zak!

    Find the lengths of BF and CF.

    i have found that BF is 4779 ... i now need to know how to find CF.

    We need repeated applications of the Law of Sines.

    In triangle ABF:\;\frac{\sin(\angle BFA)}{3000} \,=\,\frac{\sin52^o}{4779}

    . . \sin(\angle BFA) \:=\:\frac{3000\sin52^o}{4779} \:=\:0.494670906

    . . \angle BFA \:=\:29.64805186\:\approx\:29.6^o

    Then: . \angle BFC\:=\:90^o - 29.6^o\:=\:60.4^o


    In triangle BCF:\;\frac{\sin(\angle BCF)}{4779} \:=\:\frac{\sin60.4^o}{4500}\

    . . \sin(\angle BCF) \:=\:\frac{4779\sin60.4^o}{4500} \:=\:0.923403615

    . . \angle BCF \:=\:67.42885176^o\:\approx\:67.4^o

    Then: . \angle CBF\:=\:180^o - 60.4^o - 67.4^o \:=\:52.2^o


    Finally: . \frac{CF}{\sin52.2^o} \:=\:\frac{4500}{\sin60.4^o}\quad\Rightarrow\quad CF \:=\:\frac{4500\sin52.2^o}{\sin60.4^o} \:=\;4089.382738

    Therefore: . \boxed{CF \:\approx\:4089}

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