math
posted by Rose 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 .

A simple sketch will show you that that answer cannot possibly be right
Extend CB to cut the xaxis 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 xaxis
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 xaxis) = 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) = CBBA)cosØ, where Ø is our angle
6  3 = √13 √10 cos‚
cosØ = 3/√130 = .26311..
Ø = 74.74° as above.