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Math Help - Finding magnitude of u + v help?

  1. #1
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    Angry Finding magnitude of u + v help?

    Hey all!

    I was taking a quiz for my trig class and the following problem came up:

    Find the sum of u + v, given that |u| = 16, |v| = 16, and Theta = 106°.

    The magnitude of u + v is:
    19.3

    The resultant vector u + v makes the angle
    53.0 with u.

    When I tried the problem, I got 22.6 for the magnitude and 45
    ° for the angle.

    I thought that r = sqrt(u^2 + v^2), and I could use arctan=(16/16) to find the angle (at least that's what my math teacher had said).

    Any help on how they got these solutions?
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  2. #2
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    Re: Finding magnitude of u + v help?

    Doing what you have done only works if the vectors are at right angles to each other, which these aren't. (Basically, you have used the Pythagoras theorem.)
    Draw a diagram with the two vectors angled at 106 degrees to each other and draw in the vector u + v. Use the cosine rule to calculate the magnitude of u + v followed by the sine rule to calculate the angle.
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  3. #3
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    Re: Finding magnitude of u + v help?

    Quote Originally Posted by ktelyn View Post
    Hey all!
    I was taking a quiz for my trig class and the following problem came up:
    Find the sum of u + v, given that |u| = 16, |v| = 16, and Theta = 106[FONT=arial]°.
    The magnitude of u + v is:
    19.3[COLOR=#0000ff]
    The correct answer is 19.258.
    \|u+v\|^2=\|u\|^2+\|v\|^2-2\|u\|\|v\|\cos(74^o)
    Using the law of cosines and the supplement of the angle between u~\&~v.
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  4. #4
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    Re: Finding magnitude of u + v help?

    I think I know what I did wrong, LOL!

    I thought I had to put the angle they provided for the cosA part, but in reality I have to use the supplement.
    Attached Thumbnails Attached Thumbnails Finding magnitude of u + v help?-dgdgd.png  
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