Law Of Cosines Calculator

Side a:

Side b:

Angle C (in degrees):

Result:

Side c: 0

Angle C: 0

The Law of Cosines is a fundamental rule in trigonometry that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is particularly useful for solving triangles that are not right-angled. The Law of Cosines is often used to calculate the lengths of sides or the angles in a triangle when certain other parts of the triangle are known. Using a Law of Cosines calculator can quickly and accurately solve a triangle when given the appropriate information.

Law of Cosines Formula

The general form of the Law of Cosines is:

$$c^2 = a^2 + b^2 - 2ab \cdot \cos(C)$$

Where:

• a, b, and c are the lengths of the sides of the triangle.
• C is the angle opposite side c.
• a and b are the other two sides of the triangle.

The law can also be rearranged to find the lengths of the other sides or angles:

• To find side a: $$a^2 = b^2 + c^2 - 2bc \cdot \cos(A)$$
• To find angle A: $$A = \cos^{-1}\left(\frac{b^2 + c^2 - a^2}{2bc}\right)$$

Using the Law of Cosines Calculator

To use the Law of Cosines calculator, you need to know:

• Two sides of the triangle and the included angle between them (this is often called SAS, or Side-Angle-Side).
• Or, the three sides of the triangle (this is called SSS, or Side-Side-Side), and the calculator will help you find the angles.

For example, if you know:

• Side a = 7 units
• Side b = 9 units
• Angle C = 60°

You can use the Law of Cosines to calculate the length of side c:

$$c^2 = 7^2 + 9^2 - 2 \times 7 \times 9 \times \cos(60°)$$ $$c^2 = 49 + 81 - 2 \times 7 \times 9 \times 0.5$$ $$c^2 = 130 - 63 = 67$$ $$c = \sqrt{67} \approx 8.19 \, \text{units}$$

Why Use a Law of Cosines Calculator?

1. Time-Saving: The Law of Cosines involves algebraic steps, including squaring terms and calculating cosines. A calculator saves you time by performing these calculations automatically.
2. Accuracy: The calculator will ensure that all calculations are precise, reducing the risk of errors in manual computations.
3. Versatility: The Law of Cosines can solve for sides or angles in any triangle, not just right-angled triangles, making it a versatile tool in geometry and trigonometry.
4. Practical Applications: The Law of Cosines is widely used in fields like physics, engineering, navigation, and architecture, where accurate triangle measurements are required for designs, constructions, and problem-solving.

The Law of Cosines calculator is a helpful tool for anyone dealing with triangles in geometry, providing quick and reliable results for solving both the sides and angles of a triangle.