Law of cosines

Japanese school year: Math I

What you learn

Understand the Law of Cosines, which connects the three sides of any triangle with the cosine of one angle. As a generalization of the Pythagorean theorem, this rule requires basic trigonometric concepts. It is essential for determining unknown lengths and angles in surveying, 3D modeling, and vector calculations.

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Key points

Known as the Law of Cosines, this finds side $a$ from two sides $b, c$ and their included angle $A$ . It generalizes the Pythagorean theorem, matching it when $A = 90^\circ$ .

a^2 = b^2 + c^2 - 2bc\cos A

Rearranged from the Law of Cosines, this calculates $\cos A$ when all three sides $a, b, c$ are known. It is used to find angles and check whether an angle is acute or obtuse.

\cos A = \frac{b^2 + c^2 - a^2}{2bc}

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Practice 1Coming soon