Posted by **Rose** on Sunday, April 14, 2013 at 8:23am.

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 -
**Reiny**, Sunday, April 14, 2013 at 10:12am
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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