law of cosines proof and its applications

law of cosines is one of the most important law in vectors and trigonometry. law of cosine have tremendous application in the fields of mathematics physics and Pythagorean theorem is used for the determination of sides of a triangle. i.e perpendicular,base and hypotenous but the problem with pythagorean theorem is that it is valid only for right angle traingle. the best thing about the law of cosines (also known as cosines rules) it is valid for all kinds of triangle. for detail explanation watch till end.
there are total two slides in this lecture
slid first is an introductory slides which explain the Pythagoras theorem and the law of cosines the failure of Pythagorean theorem and success of law of cosines.
the second slid includes visual images for visualization of the vectors and the complete steps for derivation of law of cosines. we have proved law of cosines using vectors addition by head to tail rules and then taking the dot product of the resultant vector with itself.

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