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 Triangle Side Calculation

Details: Calculating unknown sides of triangles is fundamental in geometry, trigonometry, navigation, engineering, and physics applications.

4. Using the Calculator

Tips: Enter lengths of sides a and b in any consistent units, and angle C in degrees (must be between 0 and 180). All values must be positive numbers.

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 if I know three angles but no sides?
A: The Law of Cosines requires at least one side length. With only angles, you can determine shape but not size.

Q3: How accurate are the results?
A: Results are mathematically exact based on the inputs, though displayed with 4 decimal places for practicality.

Q4: Can I use this for non-Euclidean geometry?
A: No, this formula applies only to triangles in Euclidean (flat) space.

Q5: What units should I use?
A: Any consistent units (cm, m, inches, etc.) can be used as long as all lengths are in the same unit.