1. What is the Angle Formula (Law of Cosines)?

Definition: This calculator computes an angle in a triangle when you know the lengths of all three sides, using the Law of Cosines.

Purpose: It helps in geometry, trigonometry, and various engineering applications where triangle measurements are needed.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( θ \) — Angle opposite side c (degrees)
• \( a \) — Length of side a
• \( b \) — Length of side b
• \( c \) — Length of side opposite the angle

Explanation: The formula relates the lengths of the sides of a triangle to the cosine of one of its angles.

3. Importance of Angle Calculation

Details: Accurate angle calculation is essential in construction, navigation, physics, and computer graphics.

4. Using the Calculator

Tips: Enter the lengths of all three sides of the triangle. All values must be positive numbers that satisfy the triangle inequality theorem.

5. Frequently Asked Questions (FAQ)

Q1: What if I get "Invalid triangle" as a result?
A: This means the side lengths don't satisfy the triangle inequality (a + b > c, a + c > b, b + c > a).

Q2: Can I use this for right triangles?
A: Yes, for right triangles it will correctly return 90° when c is the hypotenuse.

Q3: What units should I use for the sides?
A: Any consistent unit (meters, feet, etc.), as long as all three sides use the same unit.

Q4: How accurate is the calculation?
A: The calculation is mathematically precise, though displayed to 2 decimal places.

Q5: Can this calculate other angles in the triangle?
A: Yes, just rotate which side is 'c' to calculate different angles.