The Cosine Law.

Cosine Law states that in any triangle following equations can be implied:

Where a is the side opposite to vertex A , b is the side opposite to vertex B and c is the side oposite to vertex C.

We can prove the above stated equations by following way:
To prove the first of these formulas , we place the triangle ABC in the standard position with the vertex A at origin and the side AB along the positive x-axis. Then, The

cordinate of three vertices A , B , C are (0,0) , (c,o) and (bCosA, +- bSinA) Respectively. The positive sign is to be taken if vertex C is above the x-axis and negative sign if it

is below x-axis.
This two figures describes how we got the coordinates ot the vertices A , B and C.

Now , using the distance formula , We have

After simplifying we get

or,

Thus we get ,

Thus we proved the first formula among 3 formulas of cosine law by simillar method we can also prove second and third one.

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