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what is cosine rulr​

Answer 1

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Answer 2

Law of cosines

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This article is about the law of cosines in Euclidean geometry. For the cosine law of optics, see Lambert's cosine law.

Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.

In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem[1]) relates the lengths of the sides of a triangle to the cosine of one of its angles. Using notation as in Fig. 1, the law of cosines states

{\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos \gamma ,}

where γ denotes the angle contained between sides of lengths a and b and opposite the side of length c. For the same figure, the other two relations are analogous:

{\displaystyle a^{2}=b^{2}+c^{2}-2bc\cos \alpha ,}

{\displaystyle b^{2}=a^{2}+c^{2}-2ac\cos \beta .}

The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if the angle γ is a right angle (of measure 90 degrees, or

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radians), then cos γ = 0, and thus the law of cosines reduces to the Pythagorean theorem:

{\displaystyle c^{2}=a^{2}+b^{2}.}

The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known.