Cosine theorem calculator

Theorems

Theorem in geometry is a proof - an argument establishing a property. A theorem is a statement that proves some property and requiring establishment. Theorems are also called lemmas, properties, consequences, rules, signs, affirmations.

Cosine theorem

Our cosine theorem calculator makes it easy for you to find the side or angle of your triangle. Simply enter the values of the two known sides and the angle between them into the calculator, and it will automatically calculate the unknown value for you. This tool is perfect for students, engineers, architects, and anyone else who needs to calculate the side or angle of a triangle.

What is Cosine Theorem?

The cosine theorem, also known as the law of cosines, is a mathematical formula used to find the side or angle of a triangle. The formula relates the lengths of the three sides of a triangle to the cosine of one of its angles. This formula is particularly useful when working with non-right-angled triangles.

Cosine Theorem Formula

The formula for the cosine theorem is:

a = \sqrt{b^2+c^2-2bc*cos(\gamma)}

Where a, b, and c are the sides of a triangle, and γ is the angle opposite side a. The formula can be rearranged to find any of the three sides or any of the three angles of a triangle.

Example

Let's look at an example of how to use the cosine theorem formula to find the side of a triangle:

Suppose we have a triangle with sides a = 5, b = 7, and an angle β = 45 degrees. To find the length of side c, we can use the cosine theorem formula:

c = \sqrt{b^2+a^2-2ba*cos(\beta)}

c = \sqrt{7^2+5^2-2*7*5*cos(45^0)}

c = 4.95

So, the length of side c is approximately 4.95.

Conclusion

In conclusion, the cosine theorem is an important formula for finding the side or angle of a triangle. Our cosine theorem calculator makes it easy to use this formula and get your answers quickly and accurately. Whether you are a student, engineer, architect, or anyone else working with triangles, our calculator is a valuable tool to have. So, use our calculator today and make your calculations easier!