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Thread: Solve for Theta

  1. #1
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    Solve for Theta

    I need to solve for theta with only the info shown in the image below.
    Solve for Theta-trig-question.gif

    Thanks.
    Attached Thumbnails Attached Thumbnails Solve for Theta-trig-question.png  
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  2. #2
    Senior Member BAdhi's Avatar
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    is 36.00 lint is deflected $\displaystyle \theta$ from the vertical line?
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  3. #3
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    Yes

    yes the angle between the vetical line on the left and the 36.00 line is .
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  4. #4
    Senior Member BAdhi's Avatar
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    Solve for Theta-diagram.bmp

    $\displaystyle sin \theta = \frac{36cos\theta -12}{128}$

    $\displaystyle 36cos\theta - 128sin\theta = 12$
    $\displaystyle
    9cos\theta - 32sin\theta = 3$
    $\displaystyle \frac{9}{\sqrt{9^2+32^2}}cos\theta - \frac{32}{\sqrt{9^2+32^2}}sin\theta = \frac{3}{\sqrt{9^2+32^2}}$

    $\displaystyle sin\alpha cos\theta - cos\alpha sin\theta = \frac{3}{\sqrt{9^2+32^2}}$

    $\displaystyle sin(\alpha - \theta) = \frac{3}{\sqrt{9^2+32^2}}$

    $\displaystyle \theta = \alpha - sin^-1(\frac{3}{\sqrt{9^2+32^2}})$

    where $\displaystyle \alpha = sin^-1(\frac{9}{\sqrt{9^2+32^2}})$
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