Properties Of Triangles

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In a triangle ABC, the cosine rule for side a is

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1. **The Law of Cosines**: A generalization of the Pythagorean Theorem for any triangle.
2. **Formula**: $a^2 = b^2 + c^2 - 2bc \cos A$.
3. **Special Case**: If $\angle A = 90^{\circ}$, $\cos 90^{\circ} = 0$, reducing it to $a^2 = b^2 + c^2$.
4. **Alternative Form**: $\cos A = \frac{b^2 + c^2 - a^2}{2bc}$.

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