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 the lengths of two sides and the included angle in degrees. All values must be positive numbers (side lengths > 0, angle between 0-180 degrees).

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator be used for right triangles?
A: Yes, but when angle C is 90°, the formula simplifies to the Pythagorean theorem (cos(90°) = 0).

Q2: What units should I use?
A: Any consistent units (cm, inches, etc.) as long as all side lengths use the same units.

Q3: What if I know three sides but no angles?
A: You can rearrange the formula to solve for an angle: \( \cos(C) = (a² + b² - c²)/(2ab) \).

Q4: Does the angle have to be in degrees?
A: This calculator expects degrees, but the formula works with radians if properly converted.

Q5: What about obtuse triangles?
A: The law works for all triangles, including obtuse ones (angles between 90° and 180°).