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 Triangle Calculations

Details: The Law of Cosines is essential in trigonometry and geometry, used in navigation, physics, engineering, and computer graphics for solving triangles.

4. Using the Calculator

Tips: Enter lengths of sides a and b, and the included angle C in degrees. All values must be positive, and angle C must be between 0 and 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculate angles if I know all three sides?
A: Yes, the Law of Cosines can be rearranged to find angles when all three sides are known.

Q2: What's the difference between Law of Cosines and Law of Sines?
A: Law of Cosines relates all three sides and one angle, while Law of Sines relates sides to their opposite angles.

Q3: Does this work for right triangles?
A: Yes, and it reduces to the Pythagorean theorem when angle C is 90° (since cos 90° = 0).

Q4: What units should I use?
A: Any consistent units (cm, m, inches, etc.) for lengths, and degrees for angles.

Q5: Can I use this for obtuse triangles?
A: Yes, the Law of Cosines works for all triangles, including obtuse ones.