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's a generalization of the Pythagorean theorem that 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 side opposite angle C

Explanation: The formula calculates the third side of a triangle when you know two sides and the included angle (SAS).

3. Importance of Triangle Calculations

Details: The Law of Cosines is essential in trigonometry, navigation, physics, and engineering for solving triangles when you have SAS (side-angle-side) information.

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: When should I use the Law of Cosines?
A: Use it when you know two sides and the included angle (SAS) or when you know all three sides (SSS) and need to find an angle.

Q2: How does this differ from the Law of Sines?
A: The Law of Sines relates sides to opposite angles and is better for AAS or ASA cases. The Law of Cosines works better for SAS or SSS cases.

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

Q4: Does this work for right triangles?
A: Yes, when C=90°, cos(90°)=0 and the formula reduces to the Pythagorean theorem.

Q5: Can I calculate angles with this formula?
A: Yes, by rearranging the formula: \( \cos(C) = \frac{a^2 + b^2 - c^2}{2ab} \)