1. What is the Law of Cosines?

The Law of Cosines relates 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 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 fundamental in trigonometry and is used in navigation, physics, engineering, and computer graphics for solving triangles.

4. Using the Calculator

Tips: Enter lengths of sides a and b in any consistent units, and the included angle C in degrees. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Can I use this for right triangles?
A: Yes, but when angle C is 90°, the formula reduces to the Pythagorean theorem since cos(90°) = 0.

Q2: What if I know all three sides but no angles?
A: You can rearrange the formula to solve for angles: \( \cos(C) = (a² + b² - c²)/(2ab) \).

Q3: Does the angle have to be in degrees?
A: This calculator uses degrees, but the formula works with radians if you convert accordingly.

Q4: Can this calculate angles?
A: Not directly in this version, but you can rearrange the formula to find angles when you know all three sides.

Q5: What units should I use?
A: Any consistent length units (meters, feet, etc.) as long as all sides use the same unit.