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Homework Help: Dot Product, what's wrong with my method?

  1. Jan 19, 2008 #1
    Find the three angles of the triangle with given vectors.

    A(1,0)
    B(3,6)
    C(-1,4)

    I found that AB & BC are congruent, so this ends up being an Isosceles triangle and the only angle I need to find is B.

    BC=<3+1,6-4>=<4,2>
    AB=<3-1,6-0>=<2,6>

    [tex]\angle B=\cos^{-1}{\frac{20}{\sqrt{20 \cdot 40}}=45^o[/tex]

    So [tex]\angle A = \angle C = \frac{180-45}{2}=67.5^o[/tex] but this isn't correct, so what am I doing wrong?

    It's supposed to be a 45, 45, 90 triangle.
     
    Last edited: Jan 19, 2008
  2. jcsd
  3. Jan 19, 2008 #2

    Dick

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    What do you mean AB and BC are congruent? That they have the same length? I don't think so. You used that their lengths are sqrt(20) and sqrt(40). AC and BC are the two equal sides.
     
  4. Jan 19, 2008 #3

    dynamicsolo

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    Homework Helper

    Angle A is not congruent to angle C; it is angles B and C that are congruent. Check the dot product of vector AC with vector AB. (This is indeed a right isosceles triangle.) Making a picture of the situation is often helpful in keeping straight which vectors you want to look at.
     
  5. Jan 19, 2008 #4
    Thanks! I found my mistake in mislabeling my congruent sides :-[
     
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