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Math Help - HELP :::::: trigonometry PLEASE

  1. #1
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    sdgdgs
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    HELP :::::: trigonometry PLEASE

    Hello there, are you OK! I hope soooo

    Brother and sisters, this is my last problem in my project and so would you please help me and I promise you that Iíll mention your names in my project I swear to GOD

    So the problem is I want to know the lengths of the lines ( ae ), ( bf ) and ( cg )



    Where AED=20.4, BFD= 13.52, CGD=10.8546 and PD= 10.2

    Theta 1=30, Theta 2=50, Theta 3=70 and Theta 4= 90



    sincerely
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  2. #2
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    Re: HELP :::::: trigonometry PLEASE

    Hello, hgphtgi!

    I'll solve one part for you.


    I want to know the lengths of AE, BF, CG.
    where AD=20.4,\:BD = 13.52,\:CD=10.8546,\:PD= 10.2
    . . \theta_1=30^o,\;\theta_2=50^o,\:\theta_3=70^o,\: \theta_4= 90^o

    We will determine AE.
    Code:
                          o D
                        * |
                   E  *   |
                    o     |
               d  * |     | 10.2
                *   |     |
              *     |     |
            * 30O - | - - |
        A o - - - - + - - o P
          : -  x  - Q 5.1 :
    In right triangle D\!P\!A, we have:

    . . \tan30^o \:=\:\frac{10.2}{x+5.1} \quad\Rightarrow\quad x \;=\;\frac{10.2}{\tan30^o} - 5.1 \;=\;12.56691824

    Hence: . x \:\approx\:12.57


    In right triangle EQA, we have:

    . . \cos30^o \:=\:\frac{x}{AE} \quad\Rightarrow\quad AE \:=\:\frac{12.57}{\cos30^o} \:=\:14.51458577

    Therefore: . AE \;\approx\;14.5
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