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 to all triangles, not just right-angled ones.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

Where:

• \( a, b, c \) — Sides of the triangle
• \( C \) — Angle opposite side c (in degrees)

Explanation: The formula allows calculation of any side given two sides and their included angle, or any angle given all three sides.

3. Importance of the Law of Cosines

Details: This law is essential in trigonometry for solving triangles (finding all sides and angles) when you don't have a right angle. It's used in navigation, physics, engineering, and computer graphics.

4. Using the Calculator

Tips: Enter any three known values (two sides and their included angle, or all three sides) to calculate the remaining value. All lengths must be positive, and angles between 0-180°.

5. Frequently Asked Questions (FAQ)

Q1: When should I use Law of Cosines vs Law of Sines?
A: Use Law of Cosines when you have SAS (two sides and included angle) or SSS (three sides). Use Law of Sines for ASA or AAS cases.

Q2: Does this work for any triangle?
A: Yes, the Law of Cosines works for all triangles - acute, right, and obtuse.

Q3: What units should I use?
A: Any consistent units for length (cm, m, inches, etc.). Angles must be in degrees.

Q4: Can I calculate area with this?
A: Not directly, but once you have all sides and angles, you can use other formulas like (1/2)ab sin C to find area.

Q5: What if I get an error?
A: Check that your inputs satisfy the triangle inequality (sum of any two sides > third side) and angle sum (angles must be between 0-180°).