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 third side to be calculated

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

3. Importance of Triangle Side Calculation

Details: Calculating the third side of a triangle is essential in geometry, trigonometry, navigation, engineering, and physics applications where triangular relationships are involved.

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: What units should I use for the side lengths?
A: You can use any consistent units (cm, m, inches, etc.) as long as both side lengths are in the same units.

Q2: Can I use this for right triangles?
A: Yes, but when angle C is 90°, the formula simplifies to the Pythagorean theorem (cos 90° = 0).

Q3: What if I know three angles but no sides?
A: You cannot determine side lengths with only angle information - you need at least one side length.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact, though practical accuracy depends on your measurement precision.

Q5: Can this calculate angles if I know all three sides?
A: Yes, the Law of Cosines can be rearranged to solve for angles when all three sides are known.