SOLUTION: Let A = (3, 1), B = (9, 5), and C = (4, 6). The protractor tells that angle CAB is about 45 degrees. Why is it exactly 45 degrees?

Algebra ->  Triangles -> SOLUTION: Let A = (3, 1), B = (9, 5), and C = (4, 6). The protractor tells that angle CAB is about 45 degrees. Why is it exactly 45 degrees?       Log On


   

Question 1055969: Let A = (3, 1), B = (9, 5), and C = (4, 6). The protractor tells that angle CAB is about 45 degrees. Why is it exactly 45 degrees?
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
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Let A = (3, 1), B = (9, 5), and C = (4, 6). The protractor tells that angle CAB is about 45 degrees. Why is it exactly 45 degrees?
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If you just know (just studied) what the dot-product is and how to use it to find the angle between two vectors in a coordinate plane,


you can apply it and to calculate cos(CAB).


For it, calculate first the vectors CA and CB and their lengths.

On this subject, see the lessons
    - Introduction to dot-product
    - Formula for Dot-product of vectors in a plane via the vectors components
    - Dot-product of vectors in a coordinate plane and the angle between two vectors
in this site.