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 and works 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 third side of a triangle when you know two sides and the included angle.

3. Importance of Triangle Calculations

Details: These calculations are fundamental in geometry, trigonometry, navigation, engineering, and physics for solving real-world problems involving triangular measurements.

4. Using the Calculator

Tips: Enter lengths of sides a and b (must be positive), and angle C between them (must be between 0° and 180°). All values must be valid to get a result.

5. Frequently Asked Questions (FAQ)

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

Q2: What units should I use?
A: Any consistent units (cm, m, inches, etc.) as long as both sides are in the same units.

Q3: Why does angle C need to be between 0° and 180°?
A: This is the valid range for an angle in a triangle - the sum of all three angles must be exactly 180°.

Q4: What if I know three sides and need an angle?
A: You can rearrange the formula: \( \cos C = (a² + b² - c²) / (2ab) \).

Q5: How accurate are the results?
A: The calculator provides results to 4 decimal places, but real-world accuracy depends on your input measurements.