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math

posted by on .

given the points A(0,0), B(3,1) and C (1,4)
what is the measure of angle ABC
I plotted it on a gragh and got
1.46 degress. I am unsure if I am doing this question correctly. Or am I misreading it
thanks in advance .

  • math - ,

    A simple sketch will show you that that answer cannot possibly be right

    Extend CB to cut the x-axis at D
    (using the basic concept that if the slope of a line is m and the line forms an angle of Ø with the x-axis
    then tanØ = m)

    slope of AB = 1/3
    so tan BAD = 1/3
    BAD = 18.43°
    slope of CB = -3/2 , angle is obtuse
    tan (angle of line with x-axis) = 123.69°
    so angle BDA = 56.304°
    and angle ABC is the exterior angle
    and angle ABC = angle BAD + angle BDA
    = 18.43° + 56.304° = 74.74°

    or

    If you know vectors
    vector CB = (-2,3)
    vector BA = (-3,-1)

    v(CB) ∙ v(BA) = |CB||BA)cosØ, where Ø is our angle
    6 - 3 = √13 √10 cos‚
    cosØ = 3/√130 = .26311..
    Ø = 74.74° as above.

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