We also use inverse cosine called arccosine to determine the angle from the cosine value. With the Law of Cosines, there is also no problem with obtuse angles as with the Law of Sines because the cosine function is negative for obtuse angles, zero for right, and positive for acute angles. It is best to find the angle opposite the longest side first. Pythagorean theorem is a special case of the Law of Cosines and can be derived from it because the cosine of 90° is 0. Pythagorean theorem works only in a right triangle. The Law of Cosines extrapolates the Pythagorean theorem for any triangle. The cosine rule, also known as the Law of Cosines, relates all three sides of a triangle with an angle of a triangle. Calculation of the inner angles of the triangle using a Law of CosinesThe Law of Cosines is useful for finding a triangle's angles when we know all three sides. ![]() The two angles opposite to the equal sides are equal (isosceles triangle base angle theorem). Vertex coordinates: A B CĬoordinates of the circumscribed circle: UĬoordinates of the inscribed circle: IĮxterior (or external, outer) angles of the triangle:
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