SOLUTION: Given the points A (0,0), B (4,3) and C (2,9), what is the measure of angle< ABC?

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Question 1037268: Given the points A (0,0), B (4,3) and C (2,9), what is the measure of angle< ABC?
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Given the points A (0,0), B (4,3) and C (2,9), what is the measure of angle< ABC?
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Find the side lengths, then use the Cosine Law.
email via the TY note if you need help, or to check your work.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

His way will work, but it's much longer, and that's not 
the way you were taught to find the angle between two lines.

You find the slopes of AB and BC, m1 and m2,

then you use the formula for the acute angle between two lines:

tan%28theta%29%22%22=%22%22abs%28%28m%5B1%5D-m%5B2%5D%29%2F%281%2Bm%5B1%5Dm%5B2%5D%29%29

then find the inverse tangent.

From the looks of the graph, the angle you want ABC is obtuse so
you find the acute angle between AB and BC and then find its
supplement, which means you will subtract from 180°.

Answer: 108.4349488°

Edwin