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 when you know two sides and the included angle.

3. Importance of Side Length Calculation

Details: Calculating unknown side lengths is fundamental in trigonometry, navigation, engineering, and physics for solving real-world problems involving 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 (angle between 0-180°).

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 want to find an angle.

Q2: How does this differ from the Pythagorean theorem?
A: The Pythagorean theorem only works for right triangles, while the Law of Cosines works for any triangle.

Q3: What units should I use?
A: Any consistent units (cm, m, inches, etc.) as long as both side lengths use the same units.

Q4: What if my angle is 90 degrees?
A: The formula reduces to the Pythagorean theorem since cos(90°) = 0.

Q5: Can I calculate angles with this formula?
A: Yes, by rearranging the formula to solve for the angle: \( C = \cos^{-1}\left(\frac{a² + b² - c²}{2ab}\right) \).