The law of cosines calculator can help you to solve problems that include triangles. You will learn the law of cosines formula and its applications. Thanks to this triangle calculator, you will be able to quickly find the properties of any arbitrary triangle.
The law of cosines describes the relationship between the lengths of the sides of any triangle. This law generalizes the Pythagorean theorem, as it allows to calculate the length of one of the sides, knowing the other sides. It can be applied to all triangles, not only the right triangles.
The law of cosines states that, for a triangle with sides and angles denoted with symbols as in the picture above,
a² = b² + c² - 2bc * cos(α)
b² = a² + c² - 2ac * cos(β)
c² = a² + b² - 2ab * cos(γ)
You can transform these law of cosines formulas to solve some problems of triangulation (solving a triangle).You can use them to find:
a = √[b² + c² - 2bc * cos(α)]
b² = √[a² + c² - 2ac * cos(β)]
c² = √[a² + b² - 2ab * cos(γ)]
α = arccos [(b² + c² - a²)/(2bc)]
β = arccos [(a² + c² - b²)/(2ac)]
γ = arccos [(a² + b² - c²)/(2ab)]
a = b*cos(γ) ±√[c² - b²*sin²(γ)]
b = c*cos(α) ±√[a² - c²*sin²(α)]
c = a*cos(β) ±√[b² - a²*sin²(β)]
You can combine the law of cosines calculator with the law of sines to solve other problems, for example finding the sides of the triangle, knowing all of the angles.