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 calculated side opposite angle C

Explanation: The formula calculates the third side of a triangle when two sides and the included angle are known.

3. Importance of Triangle Calculations

Details: The Law of Cosines is essential in trigonometry, navigation, physics, and engineering for solving triangles when the Pythagorean theorem cannot be applied.

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 must be between 0° and 180°.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator find angles?
A: No, this version calculates the third side length given two sides and their included angle.

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

Q3: What if I know three sides and need an angle?
A: You would rearrange the formula to solve for the angle: \( \cos C = \frac{a² + b² - c²}{2ab} \).

Q4: How accurate is the calculation?
A: The calculation is mathematically exact, though practical accuracy depends on input precision.

Q5: Does this work for right triangles?
A: Yes, when C=90°, the formula reduces to the Pythagorean theorem since cos(90°)=0.