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Math Help - Trigonometry; looking for an angle! Help!

  1. #1
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    Trigonometry; looking for an angle! Help!

    My question
    I've been trying this one in and out for the past 2 hours yet I can't for the love of god get it correctly.. im suspecting an error in the books answer but might not be, thats why im asking you guys.

    The picture shows an symmetrical four sided pyramid with the measurements according to the picture. Im supposed to decide the angle RTS.

    I am only supposed to use the cossinus sentance:

    c^2 = a^2 + b^2 -2(ab)*cosV



    Attempts
    I've tried to calculate each side one by one by using ST^2 = 18^2+40^2
    This gave me the three sides ST=square(1924), SR=square(1620), RT=square(2896), thus making up the sides of the Triangle inside. This would be incorrect thoug.

    I suspect that because this is a pyramid which is symmetrical, would the sides ST and TR not be 40? Then the side RS would be (36^2+18^2)=square(1620)?

    All my attempts at this have failed and I need an outsiders view on this.

    THE ANSWER IS HERE (Highlight it)
    The answer to this damn question is supposed to be 63.9 degrees.
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    RT = 40

    ST = \sqrt{40^2 - 18^2}

    RS = \sqrt{36^2 + 18^2}

    36^2 + 18^2 = 40^2 + (40^2 - 18^2) - 2(40)\sqrt{40^2 - 18^2}\cos(T)

    T \approx 64^{\circ}
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