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 for any triangle, not just right-angled ones.

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 calculated side

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 formula is essential 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 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.

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: Can I use this for any angle?
A: The angle must be between 0° and 180° to form a valid triangle.

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

Q5: Can I find angles with this formula?
A: Yes, the formula can be rearranged to find angles when all three sides are known.