Law of Cosines Calculator
Our Law of Cosines Calculator helps you find the length of an unknown side in any triangle. Just enter two known sides and the angle between them (SAS), and we'll do the math for you. It's a fundamental tool for geometry and trigonometry students.
Length of the first known side
Length of the second known side
The angle included between Side a and Side b
Our Law of Cosines Calculator helps you find the length of an unknown side in any triangle. Just enter two known sides and the angle between them (SAS), and we'll do the math for you. It's a fundamental tool for geometry and trigonometry students.
c² = a² + b² - 2ab cos(C)
Imagine a triangle with side `a = 5`, side `b = 7`, and the included angle `C = 60°`. Using the Law of Cosines, `c² = 5² + 7² - 2 * 5 * 7 * cos(60°)`. This simplifies to `c² = 25 + 49 - 70 * 0.5 = 74 - 35 = 39`. So, `c = √39 ≈ 6.245`.
The Law of Cosines is used to find the length of an unknown side in any triangle when you know two sides and the included angle (SAS). It can also find an unknown angle if all three sides are known (SSS).
The Pythagorean Theorem only applies to right-angled triangles. The Law of Cosines is a more general formula that works for all triangles, including acute, obtuse, and right-angled ones. It essentially extends the Pythagorean Theorem.
This specific calculator is designed to find a missing side when you have two sides and the included angle. To find an angle, you would need to rearrange the Law of Cosines formula and input all three side lengths.
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