Question 1055969
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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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<pre>
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.
</pre>

On this subject, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/Introduction-to-dot-product.lesson>Introduction to dot-product</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/Formula-for-Dot-product-of-vectors-in-a-plane-via-the-vectors-components.lesson>Formula for Dot-product of vectors in a plane via the vectors components</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Vectors/Dot-product-of-vectors-in-a-plane-and-the-angle-between-two-vectors.lesson>Dot-product of vectors in a coordinate plane and the angle between two vectors</A>

in this site.