SOLUTION: Given the points A(0, 0) B(3, 1) and C(1, 4) find the measure of angle ABC?

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Question 945474: Given the points A(0, 0) B(3, 1) and C(1, 4) find the measure of angle ABC?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

Using B as the origin, then the vector BA becomes (-3,-1) and vector BC becomes
(-2,3).
You can use the dot product to solve for the angle since
BA%2ABC=abs%28BA%29abs%28BC%29cos%28theta%29
-3%28-2%29%2B%28-1%29%283%29=sqrt%289%2B1%29sqrt%284%2B9%29cos%28theta%29
6-3=sqrt%2810%29sqrt%2813%29cos%28theta%29
cos%28theta%29=3%2Fsqrt%28130%29
theta=74.7