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: The Law of Cosines is essential in trigonometry and geometry for solving triangles, navigation problems, and vector calculations. It's particularly useful for non-right-angled triangles.

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 numbers (angle between 0-180 degrees).

5. Frequently Asked Questions (FAQ)

Q1: When should I use the Law of Cosines?
A: Use it when you know two sides of a triangle and the included angle, and need to find the third side.

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

Q3: Can I use this to find angles?
A: Yes, the formula can be rearranged to find angles when all three sides are known.

Q4: What units should I use?
A: Any consistent length units (meters, feet, etc.) can be used as long as all sides use the same units.

Q5: What if my angle is in radians?
A: Convert radians to degrees first (1 radian ≈ 57.2958 degrees) or modify the calculator to accept radians.