Question

Given the points A(0,0),B(3,1),and C(1,4), what is the measure of angle ABC?

Answer 1

the easiest way here would be to use vectors

u = AB = (3,1)
v = AC = (1,4)

u•v = |u| |v| cosθ
so,
cosθ = (3+4) / (√10 √17) = 7/√170 = 0.5368
θ = 57.5°

Or,
AB slope is 1/3
AC slope is 4

tanθ = (4 - 1/3) / (1+4/3) = 11/7 = 1.5714
θ = 57.5°

Answer 2

Oops. That's angle BAC.
But that's the method; adjust the numbers