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 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 third side to be calculated

Explanation: The formula calculates the length of the third side when you know two sides and the included angle.

3. Importance of Triangle Side Calculation

Details: Calculating unknown sides of triangles is fundamental in geometry, trigonometry, navigation, engineering, and physics applications.

4. Using the Calculator

Tips: Enter 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: Can I use this for right-angled triangles?
A: Yes, but when angle C is 90°, the formula simplifies to the Pythagorean theorem (cos 90° = 0).

Q2: What units should I use?
A: Any consistent length units (cm, m, inches, etc.). Angle must be in degrees.

Q3: What if I know three angles but no sides?
A: This calculator won't work. You need at least one side length to determine triangle sizes.

Q4: Can I calculate angles with this formula?
A: The formula can be rearranged to find angles, but this calculator only finds side lengths.

Q5: What about obtuse triangles?
A: The formula works for all triangles, including obtuse ones (angles > 90°).