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Math Help - Rotation of triangle

  1. #1
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    Rotation of triangle

    Hi

    I am finding this question tough (attached), I think I may have stumbled on the answer but could do with some confirmation I'm on the right path.

    Right, so far I have found the length BC = \sqrt 82 using Phythagoras.

    Now I need to determine  sin \theta, cos \theta and tan \theta

    This is where I am stuck. It is not a right angled triangle so can I use SOHCAHTOA?
    Never the less I have attempted this way and got

     tan \theta = 1/9

    sin \theta = 1/\sqrt82

    cos \theta = 9/\sqrt82

    Which all give the same answer incidentally - is this the right approach or am I off in the completely wrong direction?

    I get the last part about the two line notation, but am not sure what values to use for x and y.


    Please help.

    Thanks
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  2. #2
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    Quote Originally Posted by Ian1779 View Post
    Hi

    I am finding this question tough (attached), I think I may have stumbled on the answer but could do with some confirmation I'm on the right path.

    Right, so far I have found the length BC = \sqrt 82 using Phythagoras.

    Now I need to determine  sin \theta, cos \theta and tan \theta

    This is where I am stuck. It is not a right angled triangle so can I use SOHCAHTOA?
    Never the less I have attempted this way and got

     tan \theta = 1/9

    sin \theta = 1/\sqrt82

    cos \theta = 9/\sqrt82

    Which all give the same answer incidentally - is this the right approach or am I off in the completely wrong direction?

    I get the last part about the two line notation, but am not sure what values to use for x and y.


    Please help.

    Thanks
    After the rotation the side B''C'' has the slope m = 0. Calculate the the slope of BC (2-point-formula of a straight line) which is equal of the tangens of the angle of rotation:

    m=\dfrac{2-1}{-4-5}=-\dfrac19

    That means you have to rotate the triangle by an angles whose tangens is +\dfrac19

    I'm not quite sure what is meant by the two-line notation. The angle in question is included by the lines with the equations:

    l_1: y = 0\text{ and }l_2:y = -\dfrac19 \cdot x
    Attached Thumbnails Attached Thumbnails Rotation of triangle-transl_drehung_3eck.png  
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  3. #3
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    Thanks so much. The drawing helped even more so I could visualise it better.
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