1. What is the Law of Cosines?

The Law of Cosines is a formula relating the lengths of the sides of a triangle to the cosine of one of its angles. It generalizes the Pythagorean theorem and works for any type of triangle.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( a \) — Length of side a
• \( b \) — Length of side b
• \( C \) — Angle between sides a and b (in degrees)
• \( c \) — Length of the side opposite angle C

Explanation: The formula calculates the length of the third side of a triangle when you know two sides and the included angle.

3. Importance of the Law of Cosines

Details: This law is crucial in trigonometry for solving triangles when you have SAS (side-angle-side) information. It's used in navigation, physics, engineering, and computer graphics.

4. Using the Calculator

Tips: Enter the lengths of sides a and b, and the included angle C in degrees. All values must be positive, and the angle must be between 0 and 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: When should I use the Law of Cosines?
A: Use it when you know two sides and the included angle (SAS) and need to find the third side, or when you know all three sides and need to find an angle (SSS).

Q2: How does this differ from the Pythagorean theorem?
A: The Pythagorean theorem only works for right triangles, while the Law of Cosines works for any triangle.

Q3: What if my angle is 90 degrees?
A: The formula reduces to the Pythagorean theorem since cos(90°) = 0.

Q4: What units should I use?
A: Any consistent units can be used for side lengths (cm, m, inches, etc.). The angle must be in degrees.

Q5: Can this calculate angles too?
A: Yes, the formula can be rearranged to solve for angles when all three sides are known.