The law of cosines can be applied to right and non-right triangles.

1. Understand the Law of Cosines: The Law of Cosines is a fundamental theorem in trigonometry that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is a generalization of the Pythagorean theorem. The formula is given by $c^2 = a^2 + b^2 - 2ab \cos(C)$, where $a$, $b$, and $c$ are the lengths of the sides of a triangle, and $C$ is the angle opposite side $c$.
2. Consider a Right Triangle: Let's examine if the Law of Cosines applies to a right triangle. In a right triangle, one of the angles is $90^\circ$. Let's assume angle $C = 90^\circ$. The cosine of $90^\circ$ is $0$ (i.e., $\cos(90^\circ) = 0$).
3. Apply the Law of Cosines to a Right Triangle: Substituting $C = 90^\circ$ into the Law of Cosines formula, we get:
$$c^2 = a^2 + b^2 - 2ab \cos(90^\circ)$$
$$c^2 = a^2 + b^2 - 2ab(0)$$
$$c^2 = a^2 + b^2$$
4. Recognize the Pythagorean Theorem: The resulting equation, $c^2 = a^2 + b^2$, is the Pythagorean theorem, which is specifically true for right triangles. This shows that the Law of Cosines simplifies to the Pythagorean theorem when applied to a right triangle.
5. Conclusion: Since the Law of Cosines holds true for right triangles (as it reduces to the Pythagorean theorem) and is explicitly designed for non-right (oblique) triangles, it can be applied to both types of triangles.